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REPORT DOCUMENTATION PAGE APRE-SR-AR-TR-O4. ONT 01 Fe 2001-32 Jan 2006 FINAL TLE RD SOT RUTGERS THE STATE UNIWERSITY JORSP. 58 BEVIER ROAD PISCATAWAY NI O8t54-2040 Bai Sadie im Plasma Pipe a100F ex &. AOTTOREY br Lebowitz [2 ERPS OR NERTON NEE TS OCTET ‘5 PERFOING ORGAMEATIONT [5 SFR OARS TOUTS RESTS? WATE AS POOR | APOSRINE 015 WILSON BLVD sume ns ARLINGTON vA 22002 10, SERENA FE962001-1.0154 rr surrCERENTaR OTE [7 DesTRRO TOW AVAECAROY BYEERERT DISTRIBUTION STATEMENT a: Uatinitae 20040914 O17 edeuaianadaicnaraadicied th ots eae Ax epproximate scaly eory was developed an implemented musically for cleulaing the spae eng Hele cote sod eles fla ofa thi cylindrical hes wr cure bee beoveen two wie parallel eleeodes. Tews ound that e average eureat dens scaled asthe reeiptrcl ofthe beat WHE When the later comes very eal ‘Tho ttl cin beam crea! tus decreases proparinaly 1 te urate whl te ta eoerent oF 4 sett beeomes eat adcpeadeto SORT TERN FS: NE OF PRET [37 RECUR PEREGCHTTON | 15-CEERTT COABRIERTION] 5, SECURIFY CASEIRERTION fF URTRWN FAST ‘OF RBORT Beran rage orapsmmact Wrelasfed Vorkesiied Upcassifed ww, Boao on FINAL REPORT AFOSR GRANT AF 49620-01-1.0154 BASIC STUDIES IN PLASMA PHYSICS 02/01/01 - o1/31 /o4 Wy Joa L, Lehowite Department of Mathereatioy and Physics HM Center Rutgers Univexsity New Brunswick, NT 05508 Principal investigator 1) Space charge limited flow of a thia electron beam confined by « strong magnetic field ‘Sn approsiuate aiuytie theory is developed and tuplementad mumerically for ea? cutatng the space charge Inited current aud clete ell of « thin eplincrinal beam or current cheet betteen tivo Wide paral elotrodes, The fo is coufied by a suicently suring magnetic field. Assuming taut the potential aad current density are almost homo- sreusous in the direction traneversal tothe dew we compute the heats eureat ané profile by a variational method. We find that Ube uverage current density scele as the retiprocal ofthe beam wish when the latter becomes very small, The tatel indica beam eansout thus decresses proportionally to its diameter while the tot! eucrnt of sheet becomes almost independent of the with in this regime, 2) Nate on a diffraction-atmplication problem ‘We instigate the solution of the equation A£(,1)—DABELe,t] ~ ANS(=.2)PEla.t), for ein a cide and S(z,t} « Gaussian stochaclic field with a covariance of a pacticalar 1 An3 RIBUTION STATEMENT A, Approved tor Public Release: Distribution Unlimited form. Tt ie shown that the coupling 2 at which { [) diverges for #1 (in auitable units), is alwaye lesa or equal for D > 0 than D = 0. 48) Behavior of Susceptible Infected Susceptible Epidemics on Heterogeneous Networks with Saturation ‘We invcotigate asturation effects in sunceptibleinfemted-aumeptibie models of the spread of epidemics in heterogencous populations, The structure of inweractions in the population i represented by networks with connectivity distribution P(k), including scale. ‘roe (SF) netwocks with power law distributions Pik} ~ R°, Cunsidering caves where the rammision of infection betwen nodes depeds oa Uheir comclivity, wo introduce # saturation function C(k) which reduces the infection transmlssion rale A across an edge lag from a node with high connectivity &. A mean-field approximation with the neglect cof degree-degree comeelation then leads to a finite threshold A, > 0 for SF networks with 27 £3. We also find, in this approxcmation, the fraction of infected individuals among those with degree & for A close to A,, We investigate via computer simulation the eontact process on a heterogeneoun regular Isttice and compare the reeults with those ebtained from mean-field theory with and without neglect of dagree-degree comtelations 4) Thue Asymptoties of the Schrédinger Wave Function in Time Pariodic Po- tentials “We study the transition te the contimeum of am initially bound quantum pattile in RE, d = 1,2,3, subjected, fort > 0, to a time perindic forcing of avbitrory megnimnde, ‘Tho analysis is carried out for compactly supported potentials, satinfying certain auxiliary coulltions. TL provides eauplote any’ formation on the time Laplace transform of the wave function, From this, comprehensive tine asymptotic properties (Rarel suznmable ‘tranteeries) follow. ‘We obtain in particular a criterion for whether the wave fnnetion gets fully delocalized (complete inisation), This xesion shows that comple inieution i gener and provides 2 ‘convenient test for particular cases, When saisfed ic impes absence of discrete spacteuam ‘and resonances of the associated Floquet operator, As an Iustration we show that the ‘parametric harmonic perturbation of # potential chosen to he any wonzoro zeutiple of the ‘unracterkstic fonction of @ msamerabie compact cot bas this property. 5) Using Kinetic Monte Corlo Simulations to Study Phase Separation in Alloys ‘Worenew recent extensions of the Kinetic Ising model used to investigate phase sepe- zation in binary alloys. Firstly, vacancies ave included to mode! the difusion of the atoms cm the microscopic scae mote sealistcally. These can change the coseeening rate and the coarsening mechanism, Secondly, the laltice i allowed to deform ening tothe diferent since ofthe atoms ond the resulting misfit beeen precipitates and matrix. The defuse bility ofthe lattice inns long-range sleatie interactions between the atoms, These change ‘te shape, orientation and arrangement of che precipitates. The growth of the precipitates suo follow (he la 8} The Asymmetric Exclusion Process and Brownian Excursions ‘We comider the totaly wyrametic exlusion process (TASEP) in one dimension in its maximal curent phaso, We show, by a2 enact caleulation, that the aon-Ganesinn part of the fuctustions of density ean be described in texms of the statistical properties of Brownian excursion, Numerical eimulasious indicate that che description in terms of a “Browalan excursion remains valid for move general one divcensonal dsiveneystems in thr ‘maximal euent phase, 7) Stability of Solutions of Hydrodynamic. Bqustions Deseribing the Scaling Lisail of « Massive Piston in an Ideal Gas ‘We analyze the szability of stationary solutions of a singular Vlasov type hydrody- ‘namie equation (HIE). This equation wan derived (ander auitabie aseumptions} aa the by: drodynamica! scaling mit of the Hamitanisu evolution of u aystor consisting ofa maative a piston Smmersed in an ideal gas of point particles io a box. We find explietexteia for lobo stabiBity at well xs clsn of sclutions that are linearly unstable for a dense set of pavameter values. We present some numerical evklence that when the mechanical seis (with a large nuvsber of particles) baa tnitisl conditions "ace t atationary stable slutins fora long tie, Cn the other band, ithe of the HE, then it stays cloge to these solution finite) state of the particle system is clase (o an unstable stationary solution of the TTB, en the mechanieal system civenges rapidly from that solution and farer appeats to da- velop long lasting periodic oscillations, We find similar (approximately periodic) soluLions cf the HE that are linearly stable. 8) On the (Boltzmann) Entropy of Noacquilibriuu Systems Boltzmann defined the entropy of a macroscopic system in a maccostate M aa the og cf the whim of phate space (number of microstste) comespondiug to Mf. This agro ith tho thermodynante enteapy of Ciazsne when AY specifies the locally conserved quaotitiee of a system ia local dioraul equiltxius (LTE). Hee we digcune Boltzmann's extopy, svolving an appropriate chote af mucro-war:abies, fr systems aot in LTE, We generalize the foremlae of Bolozmann for dilute gazes and of Resibois for hacd opbere ids and stv that for mero-varlablessateying any deterministic autonomous evohtion equation arising froen the microscopic dynamics the enreesponding Pattzmtani eaopy aust satisfy an theorem, 8) Rourler’s Law for 2 Harmonic Crystal with Self-Consistent Stochastic Reser. ‘We consider a d-dimensional armonic exyetal in contact with a stochastic Langevin type hwut bath at oach site. The temperatures of the “extorioe” left and right hent baths are at specified values Ty and Tp, respectively, while the temperauunes of the “interioc” bath fre chosen self comsistently no that there js no average flux of enexgy between them and the 4 system in the stoudy state. We prove thet this requiremant uniquely fixes the temperatures ‘and the self cousistent mystern has a unique steady state, For the infrite ayntem this state is ou of loca chermat equijbrium. The corresponding heat current satiafias Fourier’s lave ‘with o finite postive thennal conduct vty whith ean also he compmied using the Gzeea- Kubo fnemula, For the hacmonis chain {@ |) the conductivity agrees with the expen obtained by Holster, Rich ane Vizecher in 1970 who fist atudied this model, In the other Timit, d > 2, the staiouary infuite valume hent conductivity behaves as (fya) where 2s the coupling to the intermodioto noservire. We al analyze the elect of having a nom-uiforn distrbusion of tho aut ath eilngx. ‘These results ace proven lgorously by couolling the behavior of tho cnerelations in the thermodynacnic liait, 10) A Random Mateix: Model of Relaxation ‘We vonsider a tuo level yoter, Se, coupled to 2 goncsal a level stem, Sy, via a random matrix. We derive an integral zepresenatir forthe mean reduced density masrir Alt) of Sein the Veit oe, and we dently a model ofS, which poseisen more ofthe properties expected far macconcapic therm reservoirs, In pactiulay, it yields the Gibbs form for p{oo). We consider also un analog of the van Hove limit and obtain a muster equation (Markov dynamics) for the evolution of p(t} on au eppropriste time nesle 11) Absolute Continuity of Projected SKE Measures of Coupled Arnold Cat Map Lattices We study a d dimensional coupled mop lattice consisting af hyperbolic tora autoxzore ‘hiss (Arnold cet maps) thet are weak:'y coupled by an analytic map. We oumstruct the Siuai-Toelle Bowen mesons for ght stem and study its marglnals oa the tai. Wa prove that they ave absolutly coutiruows with respect to Lebesgue measure if aud ouy if due coupling satisfice a nondegesoracy condition, 12) The Boltzmann Entropy for Dense Fluids Not in Loral Bquiltbrina 5 Using computer simulations we Snvestigate the time evolution of the (Boltzzunun) entyopy of'a deuse uid not in loral equifibriam. The mscrovariablas 2 daseribing the systero are the (empiical} particle density saw} end the total nergy 5. We find thot S{f,, B) ie monotone increasing in time even when its Linetie put ie dacensing. We sxgue tha for inolated HaaiNtonian aystem monotony of S(M;) — SUM.) boul hold geucealy for “pica” (the overwhe'ming majority of) inllal nucrostates (phese-paints} Xe bulging to the initial macrostate My, satishing Jig, = Mp. ‘Thin ip » consequence ‘of Liowviie's theorem srhen Af evolves according to ar autonomova deterministic la, 13) Spuce-Charge-Limited 2d Blectron Flew Between Two Flat Electrodes in a Strong Magnetic Field An appcoximete analytic entation is constructed for the 2d space change limited emis- sion by a cothode surrounded by non emitting conducting ledges of width Latubda, An essentially exact solution (via conformal mapping] of the electrostatic probiea in secmum {is matched to the solution of a linenrizet problem in the spare charge rezion whese bound- aties are sharp due to the presence of a strong magnetic field. The cumrent density exomth Jn a matrow interval new ie edges uf the cathode depende strongly oa Lambda. We obtain sn empirica! formula for the total curtent an « finction of Lambda which extends to more general cathode geometcies 14) Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exelusion Process “We consider the asymmetric exclusion process (ASEP) in one dimension an sites Lew W, in contact st sites i= 1 and i= N with infinite particle reservoics al dbuaitine fe and my. AS ps and ps are varied, the typical manroscopie steady state densicy profile Ble), 2 C [at], obtained in the timit W = Lib — a) — 00, exhibits ehocks and phase transitions, Hore we derive an exact asymptotic expression for the probability of abserving 6 ‘an arbitrary macroscopic profile pir): Pa({o(e}} ~ exp LF oe ({eCeh Pi Pas Ps) 80 that F is the lange deviation fonctions], a quantity similar to the free energy of equilibrium ystems, We find, os in the symmetric, pure'y diffusive case q = 1 (treated in am earher work), that F is in geseral a non-local functional of p(x}. Untike the symmeuric caze, hovaver, the anymmetric cuse exbibite renges of the parameters for which F((oiz}}} is not convex und others fur which F({o(n)}} has dincontinuities in ite necond derivatives af o{c) = ple); the fiuetuatious mear Z{2) are then non-Ganssian and cannot he celeulated ‘rom the larye deviation fusction, 15) Information Loss in Coarse Gratuing of Polymer Configuratious via Contact Matrices Gontact matrices provide a coarse grained description of the configuration w af a linsor chain (polymer or random walk} on Z* : Cu) = 1 when the distance between the positions of tha ith and jth stope ara let than or equal to nome distance a and Cy(e) cotherwice, We consider models in which polyasers of Jangth AV avo weights corresponding 10 simple and celf avoiding random walks, SHW and SAW, with a the minimal perminible Aistanco, We prove that to landing order 9 , the umber of matroes equals the number of wll for SAW, but not for SAWG. The nares grained Saannon entropies for SRW agree withthe fine grained ones fr <2, but differs for n> 3 16} Transition to the Continmum of a Particle In Time-Perlodic Poluntials ‘We prast uow results fir the transition to the continuom of an iniilty bound quastum particle subject to & harmonic forcing. Using rigorous exponents] agrmptotce methods we obtnin explicit; expreesions, as generalized Borel summnable transotis, for the probability of localization in specified epatial region at time, The transiting 12 the continmen eee + for ganeral compact!y supperted potentials in one dimension and ‘our results extend easily to higher dimensional systems with sphetical eyimmetry. This of course implica the abserce of disrote spectrom of the corresponding Flequet operator. 17) Hydrodynamics of Binary Fiuid Phase Segregation Starting with the Vissor-Bultrmann equation for a binary Enid mixta, we derive ae equation for the velocity fsld w when the system fe segregsted into two phases (et Jow temperatures) with « sherp interface betmeen them. uw satises the incompressible Naevier-Stolas equations together with a juenp boundary condition for the pressure across ae intecfare which, ip tora, moves with a wleciny given hy the norms component of 1u. Numerical simulations of the Viesev-Boltzmsnn equations for shear flows patel and perpendicular to the interface in a phase segregated mbuture support thie snaty expect similar behavior in real Hid snixtures. 18) Eee Energy Minimizers for a Two-Specles Model with Segregs ‘Liquid-Vapor Trans We at ‘the comistence of phases in a two-spaciea mode! whose free energy is given Dy the eealing linnie of a aystem with long range interactions (Kae potentia's} that are arlraclive Letwuen particles ofthe mame spurien and repulsive between different species. 19} Generation of Primordial Cosmological Perturbations from Statistical Me chanics Models ‘The inital conditions desaibing veel Askustions for the formacian of sceucture in standard cosmological mocels, ie, the Harsison-Zeldovich distribution, have vety charac- teint “ouper-homogeneous* properties: they aze statictial’y translation invariant and ‘aptropic, and the varience of the mass fluchaions ‘b a region of volume ¥- grows more Slowly than V. We discuss the geometrical onstruction of distributions of poines in 4/ * ‘with sinilar properties encountered in tiling and in atistical physica, eg. the Gibbs distribution of a one-component systom of chargod patticls in a uniform background fone- component plasma (OOP}], Modifications of the OCP can produce oqullbeium comelatiems of the kind scmumed in the cosmological context. We then describe how such systems can 8 ‘be used for the generation of init! conditinns in gravitational N-hody simulations 20) Exact Free Energy Functional for a Driven Diffurive Open Stationary Nonequilibrium System We vbtaiu ube exact probability expl-LEn(e)})] vf finding « macreaopic density profile the siae of the systom E> 20. F, whieh plays the role of a nonequilibrium free energy, in the stationary nonequilitrivm mate of mx open driven diffusive stem, when hse a very diferent structure ftom that found in the puraly diffusive ence. As there, Fie ‘oniocal, but the shocks ard dynamic phase transitions of the driven ayetem are relected in non-convedly of F; im discontinuities in ius wand derivatives, and im mor-Ganesian fluctuations in the atesdy stare, 21) Decay Versus Survival of a Localized State Subjected to Harmonie Forcing: Exact Results ‘We investigate the eurvial probebilicy ofa locelized 1D quautuus gurtote subjveted to u time-dependent potenti! ofthe foam ri}{)xinut with Ue} = 26(e—0} or Uke} = 2i(e ~ a} ~ 28{2-4 2), The particle a nially i» bound state produced hy the binding potetlal ~25(2): We prove that this probability goss to aeto as t > oc foe alata values of 7, aud a, ‘The diay i italy wxpanentisl followed by a #7? lew if 6 not close {6 resonances and + is stalls otherwise the exponential disappears and Ferns golden rule file. For exceptional sets of parameters 7, w and the survival probability nove: decays to zero, comeponding tn the Flequet operator having a bound stise, We show sinlar beluioe even i the absence of binding potential» persitirg a eee particle to be trapped by harmonically oscillating delta funetion potential 22) Dynamics of a Massive Piston in an Idea) Gos: Oscillatory Mation and Approach to Eat