Sudare subacvatică

Sudarea subacvatică este sudarea realizată sub nivelul apei şi reprezintă operaţia de îmbinare a două piese metalice prin încălzire locală.

Datorită interesului crescut din domeniul intervenţiilor subacvatice pentru întreţinerea, controlul şi repararea instalaţiilor, construcţiilor şi structurilor metalice imersate de importanţă deosebită în industrie cum ar fi conducte subacvatice, platforme offshore, construcţii hidrotehnice, nave etc, sudarea sub apă reprezintă unul dintre mijloacele de bază la care se face apel.

Operaţiile de sudare subacvatică se pot efectua fie în contact direct cu apa, procedeul numindu-se sudare în mediu umed, fie într-un spaţiu uscat fără contact cu apa, procedeu care poartă denumirea de sudare în mediu uscat.

Sudare în mediu umed (în apă)

Sudarea în apă

Sudarea în mediu umed sau în apă, este procedeul cel mai cunoscut şi cel mai aplicat la lucrările de reparaţii subacvatice precum şi la cele de ranfluări de nave. Sudarea se face cu arc electric, în apă, rezultând o îmbinare sudată cu caracteristici mecanice apropiate de sudura realizată la suprafaţă.

Lucrările de sudare subacvatică se efectuează atât în apă sărată cât şi în apă dulce.

Scurt istoric

• Primele încercări de sudare cu arc electric sub apă datează din anul 1802 când Sir Humprey Davy a arătat că un arc electric imersat în apă continuă să funcţioneze.
• În anul 1898, alţi cercetători au demonstrat posibilităţile de prelucrare a materialelor metalice sub apă, utilizând electrozi din sârmă, însă rezultatele obţinute au fost mediocre.
• În anul 1907 suedezul Kjellberg brevetează electrodul de sudură cu înveliş, asigurând ridicarea calităţii îmbinărilor sudate.
• În anul 1917, Amiralitatea Britanică a întreprins unele cercetări şi a demonstrat că se poate depune metal sub apă. Aceste încercări de sudură au fost efectuate în scopul de a repara, mai rapid, bastimente şi nave de război avariate.
• După această dată, s-au efectuat cercetări susţinute privind sudarea subacvatică în mai multe ţări ca S.U.A., Germania, Anglia, Franţa, fosta U.R.S.S. şi Japonia.
• În timpul celui de-al doilea război mondial, au fost folosiţi pentru prima dată electrozi înveliţi şi protejaţi cu un strat de lac. După cel de-al doilea război mondial, cercetările iau amploare ca urmare a necesităţii reparării şi scoaterii la suprafaţă a navelor avariate sau scufundate în timpul războiului.
• În anul 1946 Van der Wiligen utilizează electrozi înveliţi, acoperiţi cu diverse substanţe hidroprotectoare.
• În anii ’60, ca urmare a dezvoltării industriei de foraj marin offshore, creşte semnificativ interesul acordat sudării subacvatice în mediu umed, precum şi apariţiei şi dezvoltării unor publicaţii de specialitate.
• În anul 1970, a fost realizată prima intervenţie de sudare subacvatică în mediu umed, în apă dulce, pe construcţia metalică a unui doc, de către firma Chicago Bridge & Iron Co.din S.U.A.,
• În anul 1971 s-a efectuat prima reparaţie la o structură marină offshore utilizându-se procedeul de sudare în mediu umed. După anii ’70, industria şi firmele specializate pe plan mondial în lucrări tehnice sub apă, au început, în mod constant, să utilizeze procedeul de sudare în mediu umed.

În România, la Institutul de Sudură şi Încercări de Materiale din Timişoara s-au efectuat numeroase cercetări asupra diverselor procedee de sudură atât la suprafaţă, cât şi sub apă, şi s-au realizat mai multe echipamente specifice. În cadrul Universităţii Dunărea de Jos din Galaţi s-au pus la punct diferite instalaţii complexe, cum ar fi instalaţie de sudură subacvatică cu uscare locală şi simulatorul de sudare subacvatică hiperbară etc.

Particularităţi ale sudării în mediu umed

La realizarea operaţiei de sudare electrică sub apă, prezintă o deosebită importanţă procesele chimice, fizice şi tehnologice care au loc în timpul acestei operaţii.

Stabilitatea arcului electric

Stabilitatea arcului electric depinde de procesele chimice, fizice şi tehnologice determinante ce au loc în desfăşurarea operaţiei de sudare electrică subacvatică.

Procese chimice

• Influenţa salinităţii apei – procesul de sudare în apă sărată are o desfăşurare mai stabilă decât în apă dulce, stabilitatea procesului de sudare subacvatică creşte cu mărirea salinităţii apei;
• Interacţiunea cu oxigenul;
• Interacţiunea cu hidrogenul.

Procese fizice

• Existenţa pungii de gaze, creată de arcul electric subacvatic
• Influenţa vitezei de răcire
• Efectul adâncimii (presiunii hidrostatice)

Procese tehnologice

• Sudabilitatea – este în funcţie de mai mulţi factori cum a fi:

• • Condiţiile de sudare:

– natura curentului electric: direct;

– tipul învelişului electrodului: rutilic, acid sau bazic;

– proprietăţile substanţei hidroizolante: etanşeitate, rigiditate, prezenţa elementelor ionizante;

– diametrul electrodului: maximum 4 mm;

– influenţa presiunii hidrostatice.

• • Procesele din zona topită:

– solidificarea: rapidă;

– pătrunderea: depinde de curentul de sudare şi creşte proporţional cu presiunea hidrostatică;

– defectele în cordon: incluziuni de zgură şi pori, numărul porilor creşte cu creşterea presiunii hidrostatice, iar la aceeaşi presiune depinde de intensitatea curentului de sudare, de natura şi tipul substanţei hidroizolatoare;

Echipament

Echipamentul care se utilizează pentru sudarea pe uscat este utilizat şi la sudura subacvatică în mediu umed : sursa de curent electric, cabluri electrice, electrozi, portelectrod şi accesorii.

Sursă de curent electric

Se utilizează numai surse de curent continuu de maximum 500 A. Arcul arde mai stabil la folosirea curentului continuu decât în cazul curentului alternativ, deoarece curentul continuu descompune apa în ioni înaintea amorsării arcului.

Sursele de curent continuu pot fi generatoare de sudare antrenate de motoare electrice sau de motoare cu ardere internă.

Cabluri electrice

Pentru conducerea curentului electric la portelectrod şi la clemele de contact ale piesei de lucru, se folosesc cabluri flexibile de sudare din CuE, de construcţie multifilară din sârme foarte subţiri de 0,2 mm diametru, acoperite cu o înfăşurare din fire de bumbac şi izolaţie de cauciuc, peste care se aplică o pânză cauciucată şi o îmbrăcăminte cu manta din cauciuc.

Electrozi

Electrozii pentru sudare subacvatică au vergeaua metalică din oţel cu conţinut redus de carbon (0,1%). Diametrul electrozilor este de 4…6 mm, lungimea de 350…450 mm, iar grosimea învelişului este de 0,2…0,25 mm.

Pentru a proteja electrozii înveliţi de apă, pe suprafaţa învelişului se aplică, prin impregnare sau imersare, o peliculă hidroizolantă. Substanţele utilizate pot fi parafină, celuloid dizolvat în acetonă, bitum, lac de cauciuc, diverse vopsele, lacuri pe bază de nitroceluloză, lacuri cu glicerină, policlorură de vinil şi răşini.

Portelectrozi

Portelectrodul serveşte la prinderea electrodului. În ultimul timp sunt tot mai des folosiţi portelectrozii combinaţi, folosiţi atât pentru sudură cât şi pentru tăiere (oxi-arc sau electrică), prin utilizarea unei mandrine interschimbabile. Portelectrozii pentru sudare trebuie să îndeplinească anumite condiţii cum ar fi:

• să fie etanş;
• să permită o bună manevrabilitate;
• să permită fixarea lejeră şi sigură a electrodului;
• să asigure o legătură electrică corespunzătoare;

Accesorii

La echipamentul de bază, sunt necesare o serie de accesorii şi scule:

• clema de contact – serveşte la conducerea curentului electric de la sursa de curent la piesa de lucru sub apă;
• întrerupătorul cu pârghie- permite cuplarea şi decuplarea rapidă a sursei electrice, la cererea scafandrului sudor;
• peria de sârmă din oţel – este utilizată pentru curăţarea suprafeţei de rugină sau de depuneri marine; poate fi manuală sau acţionată mecanic (pneumatic sau hidraulic);
• filtrul din sticlă colorată – este utilizat pentru protecţia ochilor;

Avantaje

Avantajele sudurii subacvatice umede sunt:

• flexibilitate mare în aplicaţii, scafandrul sudor putând interveni la porţiuni ale unei structuri imerse care nu pot fi sudate prin nici o altă metodă de sudare;
• cost redus, echipamentul utilizat fiind asemănător celui folosit la suprafaţă;
• mobilitate ridicată a scafandrului sudor;
• timp scurt pentru executarea lucrărilor;
• libertate mai mare în alegerea metodologiei de reparat.

Dezavantaje

Dintre dezavantajele sudurii subacvatice umede pot fi menţionate:

• calitate mai scăzută a îmbinărilor realizate, aproximativ 60…80% faţă de cele obţinute la suprafaţă;
• răcire mare a băii metalice (de 10…15 ori mai mare decât în aer);
• crater mai profund decât la sudarea în aer, conducând la dificultăţi de reamorsare;
• oxidarea puternică a elementelor de aliere (Mn, Si).

Sudare în mediu uscat

Sudarea în mediu uscat se utilizează la lucrările de sudare la care se cere o înaltă calitate a sudurii, cum ar fi cazul sudării conductelor submerse de înaltă presiune aflate la adâncime mare.

Sudura în mediu uscat se efectuează în atmosferă uscată, fără apă, la presiune egală cu presiunea mediului acvatic exterior de la adâncimea de lucru.

Sudarea în mediu uscat în condiţii hiperbare are loc într-un habitat imers uscat, complet închis, numit cheson de sudură, unde presiunea este egală cu presiunea mediului acvatic exterior la adâncimea de lucru.

Procedeele de sudare în atmosferă uscată pot fi:

• în mediu uscat, în condiţii hiperbare;
• în mediu uscat, în condiţii hiperbare, în minihabitat;
• în mediu uscat, efectuată la presiune atmosferică;
• cu uscare locală.

Sudare în mediu uscat în condiţii hiperbare

Sudarea în mediu uscat hiperbar a fost dezvoltată în special datorită progreselor realizate de scufundarea de sistem unitară şi în saturaţie la mare adâncime pentru stabilirea de programe de decompresie pentru scafandrii sudori datorită perioadelor îndelungate de timp necesare efectuării operaţiei de sudare.

Scurt istoric

• Ideea utilizării unor gaze pentru protejarea metalului topit cu arc electric aparţine lui Roberts şi Van Nuys, care în anul 1919 propun încercarea gazelor inerte (heliu, argon, azot).
• Pionierii sudării în mediu uscat, în condiţii hiperbare, au fost firmele americane Ocean Systems, Reading and Bates, Taylor Diving and Salvage Co., Ray McDermott, Sub Sea Int. şi firma franceză Comex.
• Prima sudare în mediu uscat, în condiţii hiperbare, a fost realizată în anul 1965, la o magistrală de conducte submerse în Golful Mexic, la adâncimea de 24 m.
• Firma Taylor Diving and Salvage Co. a efectuat apoi, lucrări de sudare în mediu uscat la adâncimea de 167 m şi lucrări simulate la adâncimea de 366 m, în laboratorul propriu.
• În prezent în condiţii simulate, au fost efectuate suduri în mediu uscat hiperbar la adâncimi de până la 600 m.

Metoda de sudare în mediu uscat, în condiţii hiperbare, este larg utilizată pentru îmbinarea porţiunilor orizontale ale conductelor submerse, pentru efectuarea de branşamente sau pentru montarea de vane pe acestea, precum şi pentru îmbinarea riser-ului (coloanei montante) platformei de foraj marin cu o conductă submersă. Grosimea pereţilor conductelor magistrale poate fi de 6…25 mm, iar diametrul exterior de 500…900 mm.

Numărul de treceri necesare efectuării unei suduri în mediu uscat în condiţii hiperbare depinde de grosimea pereţilor conductei.

Timpul necesar efectuării unei suduri hiperbare uscate, este în medie de 9 ore pentru un diametru de conductă de 800 mm. Aproximativ acelaşi timp este necesar pentru operaţiunile de pregătire ale conductei de sudat (curăţare, tăiere, şanfrenare).

Cele mai utilizate procedee de sudare în mediu uscat, în condiţii hiperbare, sunt sudurile Wolfram-Inert-Gas/Tungsten-Inert-Gas (WIG/TIG) şi Metal-Inert-Gas (MIG).

Sudare WIG(TIG) în condiţii hiperbare

Procedeul WIG (TIG) se utilizează la lucrările de sudare „cap-la-cap” ale conductelor magistrale submerse pentru sudarea rădăcinii şi a stratului de normalizare.

Procedel de sudare WIG (TIG) este un procedeu la care arcul electric se menţine cu un electrod nefuzibil de wolfram (tungsten in engleza) între piesa de sudat şi o sârmă fuzibilă ce se introduce în zona arcului.

Procedeul de sudare în atmosferă de gaz inert utilizând un singur electrod nefuzibil de wolfram a fost brevetat în anul 1926 de Hobart şi Devers. Datorită costului ridicat al heliului, acest procedeu a fost utilizat abia în anul 1942 de către firma Northrap Aircraft Co. pentru sudarea scaunelor de avioane.

Procedeul de sudare WIG a fost primul procedeu care a fost transferat în mediu uscat în condiţii hiperbare.

Sudare MIG în condiţii hiperbare

Procedeul de sudare MIG (Metal-Inert-Gas) este procedeul la care arcul electric se fomează între piesa de sudat şi o sârmă fuzibilă, derulată dintr-o bobină, care înaintează permanent în arcul electric, printr-un portelectrod special.

Sudarea MIG este un procedeu la care timpul de sudare este mai mare, iar randamentul ceva mai ridicat decât al procedeelor WIG sau TIG.

Utilizarea procedeului MIG la adâncimi mici nu este rentabil deoarece arcul electric devine instabil. La adâncimi mai mari (peste 70 m) arcul electric este mult mai stabil, iar sudarea devine mai uşoară.

Sudarea MIG cu impulsuri este un procedeu conex, cunoscut sub denumirea de “Hydroweld”. Sudarea în impulsuri (cu arc pulsat) se realizează prin suprapunerea a doi curenţi de sudare de valori diferite: un curent de bază, permanent, având o valoare redusă şi curentul de impuls, de valoare ridicată aplicat cu o anumită frecvenţă reglabilă peste curentul de bază. Cu acest procedeu se pot obţine îmbinări sudate comparabile cu cele realizate la suprafaţă.

Sudare cu electrozi înveliţi, în condiţii hiperbare

Electrozii înveliţi sunt folosiţi pentru efectuarea trecerilor de umplere şi a ultimului strat de sudură. Se utilizează în special electrozi cu conţinut scăzut de hidrogen.

Sudabilitatea la sudura manuală în mediu uscat, în condiţii hiperbare, cu electrozi înveliţi, poate avea următoarele caracteristici:

• creşterea presiunii ambiante de lucru conduce la degajarea unei mari cantităţi de fum;
• electrozii cu înveliş bazic dau un aspect plăcut cordoanelor de sudură;
• electrozii cu înveliş rutilic produc pori în metalul depus;
• pătrunderea creşte o dată cu creşterea presiunii ambiante;
• creşterea presiunii ambiante de lucru conduce la modificarea compoziţiei chimice a sudurii;
• viteza de răcire creşte o dată cu adâncimea de lucru;
• proprietăţile mecanice ale sudurilor sunt egale sau slab inferioare celor efectuate la suprafaţă.

Electrozi, sârme-electrod şi gaze de protecţie

Electrozii de sudură folosiţi la procedeul WIG sunt din wolfram, wolfram toriat sau aliaje de wolfram, iar electrozii folosiţi la procedeul TIG sunt pe bază de tungsten.

Electrozii de wolfram sau tungsten, se fabrică sub formă de vergele cu diametrul de 1…8 mm şi lungimea de 175 mm, cu vârful ascuţit.

Portelectrodul pentru sudare WIG/TIG este de construcţie specială pentru a permite fixarea electrodului de wolfram sau tungsten.

Sârmele-electrod utilizate pot fi pline sau tubulare. Sârmele-electrod pline pentru sudarea WIG/TIG şi MIG se produc la diametre de 0,8 mm, 1 mm, 1,2 mm, 1,6 mm ?i 2,4 mm.

Compoziţia chimică a sârmei pentru sudarea WIG/TIG şi MIG se alege apropiată de cea a metalului de bază.

Sârmele electrod tubulare pentru sudarea în mediu uscat, în condiţii hiperbare, sunt realizate dintr-un înveliş metalic umplut cu un amestec de materiale pulverulente care constituie miezul sârmei.

Portelectrodul sau pistoletul pentru sudarea MIG este de construcţie specială pentru a permite trecerea prin interior a sârmei-electrod.

Utilizarea ca gaz de protecţie a amestecului heliu-oxigen (Heliox) şi argon-oxigen (Argonox), asigură protecţie totală atât scafandrilor sudori cât şi contra contaminărilor atmosferice. HELIOX şi ARGONOX constituie atmosfere ideale pentru sudarea hiperbară uscată.

Avantaje

Sudarea în mediu uscat, în condiţii hiperbare, a fost dezvoltată foarte mult la lucrările offshore efectuate în Golful Mexic şi în Marea Nordului, oferind o serie de avantaje cum ar fi:

• securitate sporită pentru scafandrii sudori prin asigurarea unui habitat uscat, încălzit, iluminat, cu sistem propriu de control al atmosferei;
• productivitate maximă datorită posibilităţii lucrului în schimburi;
• monitorizare de la suprafaţă privind pregătirea asamblării, alinierea secţiunilor, sudarea, controlul nedistructiv etc.;
• calitate a sudurii apropiată de cea realizată la suprafaţă;
• posibilitate de aplicare a preîncălzirii sau a tratamentului termic.

Dezavantaje

Dintre dezavantaje pot fi enumerate:

• echipament costisitor, de mare complexitate şi greu de manevrat;
• durată mare de lucru;
• dacă condiţiile meteorologice şi starea mării sunt nefavorabile, desfăşurarea operaţiunii se face cu greutate, conducând chiar şi la amânarea lucrărilor.

Sudare în mediu uscat, în condiţii hiperbare, în minihabitat

Spre deosebire de sudura în mediu uscat, în condiţii hiperbare, efectuată într-un cheson, acest procedeu utilizează o instalaţie de tipul unui clopot sau turelă deschisă la partea inferioară. Clopotul poate fi construit în mai multe modele şi mărimi conform configuraţiei structurii metalice submerse la care se va executa sudura. La acest procedeu, scafandrul sudor se află în mediul umed, în apă, dispunând doar de spaţiul lipsit de apă unde efectuează sudura uscată la o presiune egală cu presiunea ambiantă (minihabitatul se află în echipresiune cu mediul acvatic exterior).

Procedeul a fost dezvoltat în anii ’70 în S.U.A. unde s-a realizat sistemul Hydrobox, pentru repararea şi sudarea în mediu uscat a unor componente ale platformelor marine. Instalaţia Hydrobox poate fi utilizată pentru sudarea unei conducte atât în poziţie orizontală, cât şi în poziţie verticală.

În incintă este introdus aer sau un amestec de gaze (HELIOX, ARGONOX) la o presiune suficientă pentru evacuarea apei şi obţinerea mediului de sudare uscat.

Sudare în mediu uscat, efectuată la presiune atmosferică

Procedeul de sudare în mediu uscat, la presiune atmosferică, are loc în interiorul unei incinte special construite, menţinută uscată la presiunea atmosferică, de 1 bar (sc.abs.). Scafandrul sudor dispune de toate condiţiile pentru executarea unor suduri cu caracteristici mecanice similare celor executate la suprafaţă.

Procedeul este aplicat la repararea conductelor submarine, la executarea de branşamente şi la conectarea riser-ului la conducta submersă, la adâncimi cuprinse între 300 m şi 1000 m. Sudarea se poate executa în toate poziţiile, cu una sau mai multe treceri.

Firma COMEX a pus la punct un sistem de sudare uscată la presiune atmosferică numit Weld’AP.

Avantaje

Principalele avantaje ale procedeului sunt:

• calitatea bună a îmbinărilor sudate,
• condiţiile bune de lucru
• posibilitatea aplicării preîncălzirii şi a tratamentului termic.

Dezavantaje

Dezavantajele procedeului sunt:

• echipamentul foarte complex, greu de manevrat şi foarte costisitor,
• personalul numeros,
• utilizarea unei nave suport prevăzută cu un sistem de scufundare la mare adâncime şi cu instalaţii de aliniere şi poziţionare,
• problemele de lansare pe timp nefavorabil sau la adâncimi mici unde este resimţită acţiunea valurilor,
• durata mare de lucru.

Sudare cu uscare locală

Procedeul de sudare cu uscare locală se efectuează direct în apă, cu echipamente construite special, care îndepărtează apa din jurul arcului electric al sudurii. Procedeul a fost dezvoltat în S.U.A., Rusia, Polonia, Japonia şi România.

Se utilizează instalaţii MIG/MAG adaptate pentru sudarea în mediu umed. Capul de sudare este de construcţie specială, fiind prevăzut cu mai multe duze concentrice prin care se trimite un gaz de protecţie (CO₂), aer comprimat încălzit şi apă sub presiune pentru răcirea pistoletului.

Aerul comprimat, uscat şi încălzit, formează un ecran protector între apă şi gazul de protecţie. Zona uscată asigură diminuarea răcirii rapide a sudurii.

Procedeul utilizează componentele aflate la suprafaţă pe nava suport care sunt:

• sursa de curent,
• panoul de măsură şi control,
• compresorul de aer,
• buteliile cu bioxid de carbon,
• componentele aflate sub apă, la scafandrul sudor: capul de sudare, containerul etanş cu sârma-electrod de adaos plină sau tubulară, mecanismul de avans şi pompa de apă.

Sudarea cu uscare locală oferă o calitate bună a sudurii, costul sudurii fiind acelaşi cu cel al sudurii efectuate în mediu umed cu electrozi înveliţi. Procedeul s-a realizat cu succes sub apă până la adâncimi de 30…40 m.

Controlul îmbinărilor sudate sub apă

Controlul îmbinărilor sudate sub apă reprezintă o etapă necesară după efectuarea sudurii subacvatice. La sudarea subacvatică principala metodă este controlul nedistructiv (N.D.T.).

Metodele de control nedistructiv sunt:

• radiaţii penetrante – cu raze X sau gamma
• ultrasunete – care se face cu ajutorul aparatelor de examinare cu ultrasunete.
• lichide penetrante – care constă în aplicarea unui lichid capilar activ penetrant pe suprafaţa de examinat, îndepărtarea penetrantului rămas în afara discontinuităţilor şi aplicarea unui material absorbant, ce absoarbe penetrantul aflat în discontinuităţi punând astfel în evidenţă, prin contrast, defectele existente; această metodă se aplică pentru depistarea defectelor de suprafaţă.
• Particule magnetice – consta in magnetizarea piesei de examinat si aplicarea unor particule magnetice ce se vor “depune” in zonele de scapari ale campului magnetic

Înainte de aceste operaţii, se efectuează o curăţire a locului până la luciul metalic folosind diverse unelte subacvatice speciale acţionate pneumatic sau hidraulic.

Clasele de calitate ale îmbinărilor sudate, pe baza metodelor de control nedistructiv sunt următoarele:

• clasa I, cu defecte interioare ce se determină cu radiaţii, cele exterioare vizual, cu lichide penetrante şi cu pulberi magnetice; se admite controlul în proporţie de 50% pentru detectarea defectelor interioare şi de 100% pentru detectarea defectelor exterioare;
• clasa a II-a la care se admite controlul interior de 25% şi cel exterior de 100%;
• clasa a III-a la care se admite controlul interior de 10% şi cel exterior de 100%;
• clasa a IV-a la care nu se face controlul interior, iar cel exterior trebuie să fie de 100%.

An influential neural model of face perception suggests that the posterior superior temporal sulcus (STS) is sensitive to those aspects of faces that produce transient visual changes, including facial expression. Other researchers note that recognition of expression involves multiple sensory modalities and suggest that the STS also may respond to crossmodal facial signals that change transiently. Indeed, many studies of audiovisual (AV) speech perception show STS involvement in AV speech integration. Here we examine whether these findings extend to AV emotion. We used magnetoencephalography to measure the neural responses of participants as they viewed and heard emotionally congruent fear and minimally congruent neutral face and voice stimuli. We demonstrate significant supra-additive responses (i.e., where AV > [unimodal auditory + unimodal visual]) in the posterior STS within the first 250 ms for emotionally congruent AV stimuli. These findings show a role for the STS in processing crossmodal emotive signals.

from the Proceedings of the National Academy of Sciences of the United States of America

Clicca sull’immagine per saperne di più sull’impresa (documento tratto dal sito http://caicalolzio.com/).

N.B.: La serata sarà a scopo benefico, a favore di Telethon.

…E prossimamente, anche in Radio Thule!

Yesterday, I related the logarithm of to a piecewise linear function . You may recall that was defined for positive reals by setting it equal to 0 at , and then jumping by whenever , for some prime and integer . At the end of the day, we got to

where . Today, we’ll analyze some more, and re-write the formula above.

When I introduced , I ended with the following formula:

where the bounds on that integral are supposed to represent a curve that “starts” at the right-hand “end” of the real line, loops around 0, and then goes back out the positive axis to infinity. I’m not good enough at complex line integrals at this point to say any more about this. But apparently if you are good at these sorts of integrals, using Cauchy’s integral formula and things you can find the so-called “functional equation”

If you then use the relation I mentioned previously:

(well, you use this for ), and one I haven’t mentioned:

and move some symbols around, you arrive at a more symmetric equation:

Notice that if you plug in the formula on the left-hand side, you obtain the right-hand side.

This function on the left-hand side apparently has poles at 0 and 1, so if we define

then we obtain an entire analytic function satisfying . Using the factorial relation for , we can re-write as

I get the impression that if you know what you are doing, then the things above aren’t tooo hard to justify. Apparently the next part is a bit trickier. Apparently, you can write

where the product is indexed over the roots, , of (so ).

If you’ve heard anything about the Riemann hypothesis, you know that the roots (the “non-trivial” ones, I didn’t talk about the trivial ones) of are a big deal. Our second formula for shows that they are (basically) the same as the roots of , and so they are the that the sum above is indexed over. The symmetric equation from earlier has a little something to say about the zeroes, and it has been shown that all of the zeroes have real part bigger than 0 and less than 1 (this is called the “critical strip”). The hypothesis (whose truth won’t affect what we’re saying below) is that all of the zeroes have real part 1/2 (this is the “critical line”). Apparently Riemann didn’t need this hypothesis for the things in his paper that introduced it, so I don’t really have much more to say about it right now. Although, honestly, I still don’t see what all the fuss is about The formulas we’ll get below and tomorrow work even if the roots aren’t on the critical line (unless I’m missing something important. If I am, please comment).

Anyway, back to the topic at hand. Let me try to convince you that it isn’t horribly unreasonable to think about writing a function as a product over its roots, as I’ve done above. For the sake of example, let (or pick your own favorite polynomial). The usual way this would get factored, in all the classes I’ve ever taken or taught, is (up to permutation) , showing that the roots are . However, if you factor a 4 out of the term, and -1 and -2 out of the other terms, you can also write . You still see all the zeroes when you write the polynomial this way. You can also see that the coefficient in the front is . So we’ve written , which is the same goal as what we’re doing with above. Incidentally, the idea of writing a function this way was also used by Euler to establish (I’ve mentioned this briefly elsewhere).

We now have two formulas for , so we can put them together to get

Recalling that our formula for , at the beginning, involved , let’s take the log of the equation above and solve for the term:

The idea is now to plug this in the formula for . Apparently if you do, though, you’ll have some issues with convergence. So actually try to do the integral in , using integration by parts (hint: ). The “” term goes to 0 and you obtain

where, as before . Now plug in the 5 terms we’ve got above for , and you get a formula for . What happens to the terms? Can you actually work out any of the integrals?

Well, you might be able to. I’m not. Not right now anyway. But I can tell you about what others have figured out (rather like I’ve been doing all along, in fact)…

It’s clear that the term drops out, because you divide by and then take the derivative of a constant and just get 0. The term with ends up just giving you , which is .

The term corresponding to the term with in it can be rewritten as

(as if that were helpful).

The important terms seem to involve the function

Of course, this integrand has a bit of an asymptote at 1, so really (in Edwards’ book, anyway) is the “Cauchy principal value” of this integral, namely

This function is, rather famously, related to approximating the number of primes less than a given bound. In fact, tomorrow I plan on having more to say about this. But back to the terms in our integral for .

The term corresponding to the sum over the roots ends up giving you

.

But apparently the dominant term is the term corresponding to . It actually gives you

So, finally, we have written

Doesn’t that make you feel better? We started with the reasonably understandable

,

and created the monstrosity above. I guess this is why I’m not an analyst. To me, it seems worse to write as this terrible combination of lots of integrals. But apparently it’s useful in analysis to have such formulas. I guess we’ll see a use tomorrow…

Rock God Cred Report:

Click here to check Ronnie Montrose’s post “Montrose” band “Gamma”…a late 70’s gem “I’m Alive”…a must have tune.

Buy “Gamma 1″…this album rocks hard, but is probably the most radio friendly stuff that Ronnie Montrose has done.  A VERY good album from start to finish.

In my graphic design studio, I work with images all day (and often well into the night), color correcting and manipulating them in Photoshop. All of the monitors in my studio are profiled and calibrated. While we can’t profile and calibrate the iPhone’s screen, we can use some of the concepts behind monitor calibration and make a simple change to help improve the results you get when you are making color moves in Photogene, PhotoForge, or other image editing apps for the iPhone. This is especially critical when you’re adjusting Color, Contrast and Lightness settings in your images.

Read the rest and more at our new digs on the web, www.lifeinlofi.com >>>

De bouwmarkt, het tankstation en de elektronicazaak, niet bepaald de meest geliefde plekken voor de gemiddelde vrouw. Toch komt hier verbetering in. In de VS zijn ze er allang achter dat het loont om dergelijke locaties vrouwvriendelijker te maken. De Amerikaanse keten Home Depot (met zo’n 670 vestigingen in de VS) besloot de winkels vrouwvriendelijker in te richten met bredere gangpaden (geschikt voor kinderwagens), beter (vriendelijker) licht, goed aangeduide en schone toiletten en meer designer brands. Ook Best Buy (een Amerikaanse winkelketen uit de typisch mannelijke branche van elektronica) schakelde over op vrouwvriendelijkere winkels door een huiselijke sfeer in de winkel te creëren. In speciale ‘family rooms’ staan de producten in een huiskamer-achtige setting, zodat vrouwen de producten in eenzelfde context zien als thuis. De Zweedse tankstationketen Preems paste haar winkels aan aan vrouwen door schonere en mooiere toiletten aan te bieden en koffiecorners in de winkel te plaatsen waar vrouwen verse, gezonde producten kunnen kopen en nuttigen. Alle drie de winkelketens merkten een aanzienlijke stijging in sales, die werd veroorzaakt door een toename aan vrouwelijke klanten. Bovendien werden de veranderingen ook gewaardeerd door de mannelijke klanten.

Uit onderzoek blijkt dat vrouwelijke klanten langer in een winkel blijven en meer geld besteden dan mannelijke klanten, dus winkeliers zijn erbij gebaat als vrouwen zich op hun gemak voelen in hun winkel.

Deze tendens is nu ook doorgedrongen in Nederland. Bouwmarktketen Gamma is van plan over te gaan op vrouwvriendelijkere bouwmarkten. Door de crisis merkt de bouwketen dat verbouwingen worden uitgesteld, maar dat decoratieve producten als verf, gordijnen en lampen wel worden aangeschaft omdat dit in verhouding goedkoper is en toch voor ‘een nieuw interieur’ zorgt. Met name vrouwen houden van hiervan. Gamma wil meer decoratieve producten gaan aanbieden, meer doen aan de presentatie van producten en de winkel gezelliger en plezieriger maken voor vrouwen. De eerste winkel die is ingericht volgens deze filosofie is de winkel in Amsterdam Zuid-Oost die op 14 juli werd geopend. Hoewel de uitstraling van de winkel vrij sober is, wordt wel een groot decoratie-assortiment aangeoden. Ook het logo is aangepast; vriendelijker met minder zware, hoekige letters. Ook de reclame-uiting die Gamma onlangs publiceerde in Opzij richtte zich specifiek op vrouwen:

Deze reclame is in ieder geval een stuk beter dan onderstaande reclame van Gamma van een paar jaar geleden…..

In de nieuwe vrouwvriendelijkere winkel van Gamma gaat het vooral om een breder aanbod van decoratieve producten.

Andere bouwmarkten zagen hun belang bij de vrouwelijke consument twee jaar geleden al in: “Commercieel directeur Rob Klifman van Praxis schat dat vrouwen nu 80 à 90 procent van de koopbeslissingen beïnvloeden. „De vrouw wil bijna altijd als eerste dat er iets gebeurt in huis”, zegt formuledirecteur Ron Kloos van Karwei. „Ze gaan veel vaker mee naar de winkel om te beslissen over de kleur van verf en het type badkamerkranen.”

Daaraan passen bouwmarkten zich aan. Praxis begon drie jaar geleden zijn winkels ‘vrouwvriendelijker’ te maken. De zaken kregen meer licht, meer kleuren en er werd mooier materiaal gebruikt. Artikelen die vrouwen belangrijk vinden, zoals gordijnen, tegels, lampen en verf, staan nu voorin de winkel. De grotere winkels hebben een cafeetje. Karwei besloot hetzelfde te doen. In juni opende die keten zijn eerste vrouwvriendelijke zaak in Apeldoorn.

“Vrouwen duwen de omzet van bouwmarkten naar een record. In april van dit jaar werd de hoogste omzet ooit geboekt: ongeveer 350 miljoen euro, maar een maand later werd dat record alweer verbroken: 370 miljoen euro. Praxis verkocht dit voorjaar rond 50 procent meer tuinspullen dan in de lente van 2006: vooral vijvers, sierstenen en schuttingen” (Bron: NRC Handelsblad).

Bakteri dan serangga bersaing dengan manusia untuk memperoleh makanan. Manusia, bakteri, dan serangga sama-sama suka makan nasi, daging, sayur, dan susu. Sayangnya, bakteri sering mencuri makanan yang disimpan manusia. Yaps, makanan yang disimpan jadi busuk dan beracun gara-gara dimakan bakteri dan serangga. Padahal, manusia harus menyimpan makanan untuk persediaan hari esok. Apakah ada cara ampuh untuk mengusir bakteri dan serangga?

Sekali Sorot, Bakteri Melayang

Slap! Slap! Bakteri dan serangga langsung tewas. Olala, kenapa bakteri dan serangga tiba-tiba tewas? Wow, rupanya ada kekuatan canggih untuk melawan bakteri dan serangga. Kekuatan itu mengeluarkan sinar yang dahsyat.

Kekuatan apakah itu? Itulah mesin sinar gamma. Sinar gamma berasal dari bahan radioaktif. Bahan radioaktif adalah bahan yang secara alami memancarkan energi. Pancaran energi radioaktif bermacam-macam. Ada yang berbentuk sinar X, sinar beta, dan sinar gamma. Pancaran bahan radioaktif dapat merusak sel tubuh makhluk hidup. Artinya, jika makhluk hidup kena pancaran sinar radioaktif terlalu lama, maka makhluk hidup bisa mati. Nah, sedikit saja pancaran sinar radioaktif dapat mematikan bakteri dan serangga. Zeeettt…. Sekali sorot, bakteri dan serangga langsung mati. Wuiii, kekuatan sinar gamma sangat dahsyat.

Dinding Super Tebal

Ilmuwan menggunakan sinar gamma untuk membunuh bakteri jahat dan serangga yang merusak makanan. Makanan yang disinari sinar gamma disebut makanan iradiasi.

Bagaimana makanan iradiasi dibuat? Hmm, makanan iradiasi dibuat dengan super hati-hati. Karena sinar gamma hanya dapat diperoleh dari bahan radioaktif yang sangat berbahaya. Bahan radioaktif ditaruh dalam kotak berlapis timah super tebal. Kotak  berdinding tebal ini disebut mesin penghasil sinar gamma. Ilmuwan harus memakai baju anti radiasi saat mengutak-atik mesin sinar gamma.

Makanan lalu dimasukkan dalam ruangan berlapis timah. Makanan dihadapkan pada mesin penghasil sinar gamma. Hihihi… makanan mirip manusia saat rontgen gigi dan tulang patah. Lalu, sinar gamma disorotkan ke makanan selama sedetik. Hasilnya, 99 persen bakteri dan serangga langsung mati!

Makanan Astronot

Uniknya, makanan iradiasi tidak beracun. Karena makanan iradiasi tidak bersentuhan langsung dengan zat radioaktif. Dosis sinar gamma yang dipakai juga tidak merusak sel makanan. Sel makanan tetap utuh sehingga gizi makanan tidak berkurang. Makanan jadi tahan lama karena tidak ada bakteri dan serangga yang merusak makanan. Badan pangan dan kesehatan dunia (FAO dan WHO) menyatakan makanan iradiasi tidak berbahaya bagi manusia.

Makanan iradiasi pertama kali dipakai untuk misi antariksa. Para astronot bekerja di antariksa yang jauh dari Bumi yang nyaman. Badan astronot dijaga betul agar tidak sakit. Kebayang enggak sih, betapa repotnya astronot jika sakit? Oleh karena itu, makanan astronot harus steril alias bersih dari bakteri dan serangga. Ssst, kata para astronot, makanan iradiasi lebih tahan lama daripada makanan panas atau beku. Rasa makanan iradiasi sama dengan aslinya.

[Sumber: http://www.konferensianak.com]

I guess it is about time to get to the zeta function side of this story, if we’re ever going to use Farey sequences to show how you could prove the Riemann hypothesis. I’ve been reading a bit of Edwards’ book, with the same title as this post, and thought I’d try to summarize the first chapter over the next few posts. I’m not sure that the content of the first chapter is hugely vital for the final goal of relating to the Farey sequences, but I wanted to try to learn some of it anyway.

I should mention, before talking about any of this, that I will not claim to know any complex analysis. The last complex analysis course I took was 5 years ago, I can’t be sure how much I paid attention at the time, and I haven’t used it since. I will be jumping over gaps of various sizes for quite a while in the upcoming posts. Perhaps sometimes I’ll mention that a gap is there. Mostly, though, what I’m after in this story is the outline, and how all of the parts fit together, as a big picture. Perhaps I’ll go back and fill in some gaps, as I understand more.

For today, let’s see if I can build up to an analytic expression of . Our starting point is the function

which is defined for real values of larger than 1. The goal is to find a nice expression that is defined on more of the complex plane, but agrees with this definition on the reals larger than 1.

To get to that point, we’ll use the function:

This is an analytic function defined everywhere except at the negative integers and 0. If you are only interested in real values of , this function is a continuous extension of the factorial function, which is only defined on the positive integers. Actually, there is a shift involved, so (Edwards blames this shift on Legendre, whose reasons, he states, “are obscure”. Edwards uses throughout, so I might make some errors). In particular, when both sides make sense.

Another relation that we’ll use is that

If memory serves (from reading Artin’s lovely little book on the function), you can obtain this by determining that the derivative of the expression on the right is 0. This tells you that is a constant, and so you can pick your favorite value of to obtain the value of that constant. Anyway, the identity I’ll use is a rearrangement of the one above, namely

.

Now, in the expression

,

substitute for some positive . Messing about with that substitution for a few minutes (and then re-writing by abuse of notation), you can arrive at

.

That in the denominator is useful for us, as that’s how it shows up in . In particular, we can obtain

That last transition coming about by summing the geometric series. There are probably some things analysts like to check in here, moving infinite sums and improper integrals past each other… I’ll let them.

Ok, we’re nearly there. Next up, you do some complex line integral and show that

.

That integral is a little weird, going “from to “. Really, we take a path that “starts at “, swings around , then goes back out to infinity. This is almost certainly one of the complex analysis things I should go back and learn more about. Since we are integrating along positive real values of , we’re working with logs along the negative real axis. Perhaps I’ll return to this integral in a future post.

Using the identity about from above, we obtain

.

We’re now at a point where we’ve (apparently) got an expression for that is analytic in the complex plane except for a simple pole at .

Le foto e i filmati ripresi durante la spedizione alpinistica UOEI/Gamma al monte McKinley – 6194 m (Alaska – Maggio/Giugno 2009) la più alta montagna del Nord America e fra le più fredde del pianeta, raccontati direttamente dai protagonisti…

Clicca sull’immagine della locandina per visitare la pagina dedicata all’evento su Facebook.

P.S.: …e prossimamente anche in Radio Thule!

“So tell me Ms. Grace, what’s your problem”

Dr.Purushothaman, Psychiatrist interrogated her with his bald head shimmering in the Tube light’s reflection

“I had a bad dream today. I’m going to die. But do not know how. The dream is actually incomplete” said Grace with worried face.

He has seen many patients with mental disorder and many other cases dealing with dreams. He could understand her. She was yet another patient who has been affected mentally by dreams and this makes her uncomfortable.

“OK, tell me what happened and what did you see in your dream. I’ll try to sort it out” said the doctor.

She started narrating,

***

Click the “Read more…” link below to read the rest of the story

I woke up from a deep sleep. My eyes felt heavy. My heart was pounding. I could feel the hydraulics of my arteries and veins that aided the traversal of blood. I was engulfed in fear.

Fear of Death !!

The room was normal. Neat, tidy and well kept. The curtains covering the window pane filled the room with bright creamy white ambience. The fan above my head was rotating silently under the magnetic flux exerted in its motor windings.

There was a table and a chair near the bed in which I was lying. I was under some compulsion of doing something. I felt as if I had to complete a couple of tasks. I opened the table’s drawer, and found a watch which had stopped working. There was a small chit in which something was written in it. It had a train’s name and the nearby railway station. I did not know how I knew that it was a train’s name and the railway station which was written in it.

I got up, came out, locked the room and started walking in the streets and caught an auto to reach the station. To my amusement, the station was deserted. I could see, not even a single soul, except a stray dog which lifted its head occasionally in response to the lonely bell man who bangs the metal plate hung outside the station master’s cabin.

I could hear the sound of the horn emitted far away in the tracks. The motion of vestibules in the tracks echoed the station roofs. I could see the headlight of the engine approaching the platform. Then I walked along the platform and got into one of the compartments. It had very few people. All of them were engrossed in the newspaper or gazing paranormally the roof of the compartment. I felt something creepy out here in this place. I plugged in my iPod and followed the other zombie looks of the passengers.

It was a 20 minute journey.

The train slowed down giving all of us hints that it is approaching a station. I got up from my seat scanned all the passengers who were sitting as if they have lost everything in life. No one was ready to get down. The train halted with a jerk. I got down the train and walked towards the exit.

In another 15 minutes, I reached the City Terminal Shopping Complex and searched for the surgical instruments shop. I really do not know why did, I searched for that.

“Oh I see, usually weird dreams doesn’t equip you with a reason for an incident to happen. It just happens”, said the doctor looking keenly on her case.

“One Surgical knife please “, I said to the shopkeeper

“Yes madam. Which one do you want?”

“The disposable carbon steel surgical knife, size 3”

“Here it is madam”

“Is it double sterilized under vacuum?” I enquired

“Of course, these days surgical equipments are sterilized under vacuum to avoid compound formation. Gamma radiation sterilization is also stopped now-a-days” He explained. “Here is a coupon for every purchase of this product. Scratch the colored areas in the coupon which will reveal a unique number. If your number appears in the weekly lot results of our surgical instruments association then you will have gifts sent to your home. Please fill out this form madam.”

I filled the form and entered the coupon number in it. I left the place after paying him the bill. When I reached the same place, where I woke up, I had a key to open the door. I entered the room and there was a cover lying in the ground. There was again a small chit in the paper which asked me to deposit the Demand draft inside the cover to the account number mentioned.

I did not know what I was doing. I quickly refreshed myself. Had a drink and left the room towards the bank. I was being operated I guess. I was walking towards the nearby bank.

Oriental Bank of India, the name board beamed in its golden yellow font beveled in a blue board. I entered the bank and waited in the queue for my turn. That’s when I saw a haphazardly dressed man entering the bank in a hurry. He was restless and took a withdrawal form from the table and stood still. His hands went up to his shirt pockets, inside his pant pockets and to his disappointment; he did not find what he wanted. I saw him approaching me with a scurry look on his face.

“Pen please” He asked. I understood his need and took out the pen from my bag with which I filled the form in the surgical company.

“Thank you very much” saying this, he hurriedly went to the table where quite a few of them have been filling up various forms. By the time he was about to complete filling it, the pen ceases to write.

“Sorry madam. The pen got over. I’ll get you a new one.”

“No that’s OK. I can manage. No need to get new one”

“No no. You helped me and it is my duty to help you.” Saying this he hurried out of the bank. I followed him shouting not to take pains of getting a new pen. By the time I reached to exit, he had reached the road and crossed it looking back. The moment he found himself in the middle of the road, a big Lorry carrying cement mixer was in close encounter to him and he did not get any split second to understand what was going to happen.

The lorry ran over him in full speed leaving the wriggling body mercilessly in the middle of the road. I couldn’t register anything happening in quick succession. By the time, I reached him, a considerable amount of crowd gathered around him. His head bleeding vigorously sent chilling impulses in everyone’s spine.

I reached him, and looked around to get any help from the people around but it is of no use. I kneeled down took his hands and…err..I don’t remember after this.

“What you forgot? Try recalling it again. May be you’ll remember the words spoken by him” said the doctor

“No…I’m not able to recall”. I squirmed in the seat unable to recall what happened after that.

There was a silence which filled the room for few minutes.

“He said something about my Death……” I broke the silence. But do not know what exactly he said. Am I going to die? Please doctor, help me. I’m not able to sleep in peace”

***

Purushothaman thought,

Well, people are affected mentally due to many cases and weird dreams are one of those cases which need patience and some consulting which can free them from the mental trauma that they undergo out of it. There is no solution for dreams as they occur randomly based on our thoughts and our desires. Few scenes or incidents that impact our mind, stays there in the memory for some time and our mind keeps on thinking about it as how we play the song or a video clipping again and again if we like it so much. I think this is one of the cases which needs proper mental treatment and not a medical one. Probably, I can speak to her after sometime, so that I can give her some relaxation techniques to keep her captivated mind away from these thoughts.

“Please wait outside in the couch. Have something in the canteen. Meet me after an hour. I’ll prescribe you what you need as of now” said the doctor

“Thank You doctor. Meet you after an hour said the lady and left the room.

“Next Please” said the doctor and pressed the buzzer.

A middle aged man who looked more worried than the world busiest person in the world entered the room.

“Please be seated” said the doctor. “Your name please” asked the doctor and opened his prescription pad.

“Ahmed. Ijas Ahmed”

“Hi Ijas, tell me now. What’s your problem?” the doctor adjusted his bifocal lensed spectacle frame and started listening.

***

“I work for a surgical equipments manufacturing and distribution company. I had a weird dream yesterday”

“What?….You too? Weird dreams? What the fuck?” the doctor could not believe what he just uttered. “Sorry. I was in a tension. I shouldn’t have used such word” he apologized.

“That’s OK doctor. Not an issue” Ijas said

So, last night I went to bed after a bad day at office. I slept late after a small fight with my wife. I did not return home in time. The worst part was the dream. In my dream, I was talking to my wife sitting in my cabin. Don’t know exactly what I spoke, but I was talking to her something serious.

Just then my desk phone rang and I picked up the line. It was my secretary!

“Hello dear, wazzup?” came the female voice from the other side.

“No…nothing…I’m in office”

“Come home tonight for dinner and you know what for…(laughing)”

“OK..ugh…I’ll talk to you later. Bye for now” I said.

“Hey what happened to you? Are you alri…”(Phone gets disconnected)

Just then my boss entered the room and called for meeting. I asked my wife to leave and assured her I’ll join her sometime later.

The meeting went for an hour I guess. I don’t remember anything. He was discussing about promotional offers for the product. Introduction of the coupons, gifts and bumper prizes were discussed. I was asked to deliver the proposal of this promotional offer. My head was spinning like hell. Once the meeting was over, I came out of the room. I knew that I’m in dream. The surrounding was not real. It was appearing as if it is simulated.

I came out of the meeting hall to find myself isolated in seashore. The sun was setting on the west. I could see the silhouette of an old dilapidated bungalow. I looked back in an anticipation to get back to the meeting hall. But to my disappointment, I found a vast beach covered with sands and stones.

I walked on the sands along the shore. I was thinking what to do next. A series of unrelated events were happening to me. I was pondering over lot of things. Something nudged my feet under the sand. I bent down to pick it up. But it did not come. It was buried in the sand and only a part of the object was visible.

I bent down to pull it out. I could hold it well with my fingers. It seemed to be some cylindrical object made of glass. I dug the wet sand around the object to bring that out. It was an ordinary transparent liquor bottle. I have read this in fairy tales, in which the hero will pick up a bottle from the sea and when he opens the bottle, a ghost will appear from inside and it will thank the master for releasing him from the bottle in which it was held captive for years together.

In an anticipation to see something different, I opened the bottle to find a small cover rolled inside the bottle. It was a normal long cover envelope. I took out cover to see a small sheet of old paper and a demand draft and an address to which it has to be delivered. I was wondering, how this place can have any relation to this demand draft. I myself felt rubbish at this dream. The chit was written in a scribbled handwriting. It was an order to deliver that and there was one last sentence

Thou shall meet demise in any case

My heart stopped. I was cursing myself as to why did I open this bloody bottle to see different things. I took the bottle in hand and smelled the opening. I could feel the world around me spinning like a vortex. When I came back to senses, I was standing outside the door which seemed to be an apartment. I was standing outside a locked door. I found the cover in my shirt packet. I slid the cover through the vent in between the door and the floor. Once the thing was done, I was again occupied with the thought of death. I turned back to find my secretary standing in her tube tops and her black velvet skirt. Her looks were attractive in that costume. She showed her mobile in which she had my wife’s number.

“Oh my God….quite a twisty incidents you are coming up with. OK go on. What happened next?” enquired the doctor.

She demanded money. She wanted immediately. She put her hand around my neck and came closer and said, “Sweety, if I’m not getting it now, then I have to place this demand to your wife. I still have her number. Then she may come to know about our weekend dinner. So decide which is good for you and act accordingly. I’ll call you back after an hour darling. Meet me at my place. Cya…baby”.She left the place, telling this. I kept looking at her, getting down the stairs. She gave one final look before disappearing in the swirl steps.

I was already confused on what was happening around me…

“Yea even I’m confused on the series of events”, the doctor interrupted.

I climbed down the stairs, caught a taxi and reached the bank which was 30 minutes away from that place. I had to wait for a long time for the taxi. The journey appeared to be a long one, though it was a half an hour one. Already lost half an hour, I had to get money for my secretary in another half an hour. I hurried to the bank.

I entered the bank and looked blank. I did not know what to do. Withdrawal, yes I have to withdraw money. I didn’t have the debit card. I slid my hands into my shirt pocket, then into my pant pocket in search of pen. It wasn’t there. I looked at the crowd. I could see a lady staring at me. Thought I could get some help from her

Doctors eyes broadened and his jaws dropped. This was the incident narrated by Grace. He couldn’t believe what he was hearing. He was apparently listening to the Grace’s dreams in this man’s version. And he is fully aware that she is going to tell how this man is going to die and what did he tell about Grace’s Death. Purushothaman became curious and listened to him more carefully

“Pen Please” I asked approaching her. She was looking at me in amusement. I didn’t care for that, because I was in a more serious situation and had no time to ponder over her gaze. She gave me pen.

“Thank you very much” I said in response and I hurriedly went to the table where quite a few of them have been filling up various forms. By the time I completed filling it, the pen ceased to write. It was over. I thought it would be bad if I give her back the empty pen. So I gave a thought to get her a new pen.

“Sorry madam. The pen got over. I’ll get you a new one.” I said.

“No that’s OK. I can manage. No need to get new one” She gave a smiling response.

“No no. You helped me and it is my duty to help you.” Saying this I hurried out of the bank and had reached the road and crossed it looked back. The moment I found myself in the middle of the road, something was ringing loudly near my ears. I felt disturbed. The whole mind got upset and was couldn’t concentrate on what I was about to do or what I was up to currently. Suddenly a gush of air struck my face and I woke up in my bed as the alarm rang 6.00 AM sharp near my bed.

***

“Now, tell me doctor, I was going to die. I don’t know when. But I’m sure whenever I happen to hit the bed in the future; this nightmare will haunt me like hell. Please help me to come out of this mental torture.”

Purushothaman was disappointed as this man was not able to tell about her death. His dream ended incomplete!

“That’s it?”

“Yea. I woke up after that. I did not know what happened” said Ijas

“Hmmm…” As a psychiatrist, he has handled patients with mental disorder, but this is not a disorder which can be cured with medicines. This is a mental agony and the fear of death which causes such dreams and people ebb out with such complaints.

He pressed the buzzer twice. A lean dark man in his white pants and shirt appeared into the room.

“Send that lady inside” Dr requested the attender in his low voice.

The lady appeared in front of the doctor. Purushothaman asked her to sit in the chair beside Ijas.

“Well Grcae…He is Ijas. Human mind is one complex creation in this world and we cannot judge how it behaves in bad times. When cannot control it in extreme cases. When we are angry, we tend to lose our sense and we shout. We do all extreme things which our mind commands us to do. But it is more complex when same incidents happening in one’s dream are seen by another human being in their own version. They have a different incidents lined up in their mind. There are little chances that two persons who see same incidents happening in the dream can actually solve each other’s problem”

“Oh I see” Grace interrupted.

“So it may turn out to be a surprise for you, the one which I’m going to tell you. He was the one whom you saw in your dreams. The haphazardly dressed man, who was searching for the pen”

Hearing this both Grace and Ijas gave a bewildered look at each other. Purushothaman spoke to both of them.

“Today I heard the two dreams which meet at a point involving two different persons and the rarest cases of happening that, both the persons involved in the incident are here”

“Oh My God. I couldn’t believe this” Ijas stumbled upon the table and his voice so strong.

You have to believe Ijas. Grace saw your death. You died in the lorry accident which took place outside the Oriental bank. Now I do not have any answers for the Grace’s question. She was also in the fear of death. And the mode of her death was in your mouth when you were about to die”

“My mouth…? I didn’t know how I died and I woke up before I could see my death. How can this be possible?” shouted Ijas in rage. The doctor understood the situation getting worse and in an effort to calm him down, he spoke to Grace.

“OK guys. You people need some rest. I’ll answer all your questions this evening after some examination.

He took both of them to the adjacent room which was quite dark. It had a fewer seats and a table. A large neon bulb was hanging in the middle of the room. Doctor asked Ijas to occupy the chair in the center of the room. Grace sat in the couch, in the corner of the room. Purushothaman switched off other sources of light except the one in the center and brought a syringe full of greenish dull liquid containing Non-benzodiazepine compound and injected it in his arms bringing him to a temporary state of unconsciousness. Grace was looking at all this from the corner of the room and a slight smile appeared in her lips packed with sarcasm. She emitted an ethereal smile.

Doctor was trying to hypnotize Ijas and trying to read his subconscious mind. He was fully focused on how to get things out of his mind so that, this case can be handled with ease. There was no one in the room expect Grace, Ijas and Doctor Purushothaman. Suddenly he could feel some one touching him from behind. He raised his bent body and turned back to see Grace standing close to him. She still had the eerie smile in her lips.

“Wh…What Grace? What do you want?” turning his head towards her, he asked with a tinge of fear in his eyes. Before he could throw another question to her, she took out the Surgical Knife which gleamed silverfish in her hands, from her hand bag, and made a quick incision in the back of his neck. It made a silent mark leaving behind a thin line of blood. In a few minutes, blood started flowing from the incision that was made. Before he could gather strength, there went another flick of the knife which made cuts in his skin, below his head, without any friction of muscles. The cuts were very flamboyant and it made a deep mark in the tissues, cutting each and every vein apart, running from the spine to his brain. It was the time for her to act smart. When the doctor fell down holding his head, she quickly bent down and made a deep incision in his right chest leaving him bleeding and which will cause immediate death

Purushothaman’s vision blurred as he was subjected to Class IV Hemorrhage which attributes to the loss of more than 40 percent of the circulating blood volume. He could still feel the devastating pain in his head. Death was waiting at the door.

***

“Aaaaaaaaaaaghhhhh. Noooooooooo. Please don’t do this. Why are you doing this?.Aaaaaaaaaaghhhhhhh” Shouted Purushothaman twitching in the bed holding his head tight.

“Puru…hey you. What happened?”, Janaki held his hands tight pulling him close to her. She sat on the bed near him, removed the blanket and agitated him to wake him up. He woke up with pounding heart, his face fully drenched in sweat. He looked left and then right. Opened the water bottle near the bed and gulped few ‘ml’s of it then sighed. He touched his back of his neck and looked at his fingers in search of blood.

Janaki couldn’t understand her husband’s behavior.

“What happened? Why the hell are you shouting in this night?”

“No…nothing. I’m fine. I was just out of shock. It was a nightmare. I’m fine. I’m fine”

“Tell me what happened?”

“No it was just a dream. I saw weird people in my hospital. They came to me for consultation….then…then, they were…Surgical Knife…”

“Oh…again with your weird patients!!!! I’ve told many times not to spend too much time on those psycho people whom you call your patients. Now they are coming in your dreams too.?? It is really weird…”

Janaki shouted at her husband with a false anger and kissed him good night.

“Yea. It is a weird dream”

THE END