Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Single-molecule thermodynamics: the heat distribution function of a charged particle in a static magnetic field

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems-the heat exchanges of the particle alone-because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Tensile flow behaviour of 2.25Cr-1Mo ferritic steel base metal and simulated heat affected zone structures of 2.25Cr-1Mo weld joint

Tensile tests in the temperature range 298 to 873 K have been performed on 2.25Cr-1Mo base metal and simulated heat affected zone (HAZ) structures of its weld joint, namely coarse grain bainite, fine grain bainite and intercritical structure. Tensile flow behaviour of all the microstructural conditions could be adequately described by the Hollomon equation (sigma = K-1 epsilon(n1)) at higher (> 623 K) temperatures. Deviation from the Hollomon equation was observed at low strains and lower (< 623 K) temperatures. The Ludwigson modification of Hollomon's equation, sigma = K-1 epsilon(n1) + exp (K-2 + n(2) epsilon), was found to describe the flow curve. In general, the flow parameters n(1), K-1, n(2) and K-2 were found to decrease with increase in temperature except in the intermediate temperature range (423 to 623 K). Peaks/plateaus were observed in their variation with temperature in the intermediate temperature range coinciding with the occurrence of serrated flow in the load-elongation curve. The n(1) Value increased and the K-1 value decreased with the type of microstructure in the order: coarse grain bainite, fine grain bainite, base metal and intercritical structure. The variation of nl with microstructure has been rationalized on the basis of mean free path (MFP) of dislocations which is directly related to the inter-particle spacing. Larger MFP of dislocations lead to higher strain hardening exponents n(1).

Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

Ferromagnetic transition and specific heat of Pr(0.6)Sr(0.4)MnO(3)

The critical properties of orthorhombic Pr(0.6)Sr(0.4)MnO(3) single crystals were investigated by a series of static magnetization measurements along the three different crystallographic axes as well as by specific heat measurements. A careful range-of-fitting-analysis of the magnetization and susceptibility data obtained from the modified Arrott plots shows that Pr(0.6)Sr(0.4)MnO(3) has a very narrow critical regime. Nevertheless, the system belongs to the three-dimensional (3D) Heisenberg universality class with short-range exchange. The critical exponents obey Widom scaling and are in excellent agreement with the single scaling equation of state M(H,epsilon) = vertical bar epsilon vertical bar(beta) f(+/-)(H/vertical bar epsilon vertical bar((beta+gamma)); with f(+) for T > T(c) and f(-) for T < T(c). A detailed analysis of the specific heat that account for all relevant contributions allows us to extract and analyze the contribution related to the magnetic phase transition. The specific heat indicates the presence of a linear electronic term at low temperatures and a prominent contribution from crystal field excitations of Pr. A comparison with data from literature for PrMnO(3) shows that a Pr-Mn magnetic exchange is responsible for a sizable shift in the lowest lying excitation.

Transport processes in one component plasmas using Landau equation

A system of transport equations have been obtained for plasma of electrons and having a background of positive ions in the presence of an electric and magnetic field. The starting kinetic equation is the well-known Landau kinetic equation. The distribution function of the kinetic equation has been expanded in powers of generalized Hermite polynomials and following Grad, a consistent set of transport equations have been obtained. The expressions for viscosity and heat conductivity have been deduced from the transport equation.

Heat and mass transfer and chemical transformation in a cerium nitrate droplet

This paper deals with the thermo-physical changes that a droplet undergoes when it is radiatively heated in a levitated environment. The heat and mass transport model has been developed along with chemical kinetics within a cerium nitrate droplet. The chemical transformation of cerium nitrate to ceria during the process is predicted using Kramers' reaction mechanism which justifies the formation of ceria at a very low temperature as observed in experiments. The rate equation modeled by Kramers is modified suitably to be applicable within the framework of a droplet, and predicts experimental results well in both bulk form of cerium nitrate and in aqueous cerium nitrate droplet. The dependence of dissociation reaction rate on droplet size is determined and the transient mass concentration of unreacted cerium nitrate is reported. The model is validated with experiments both for liquid phase vaporization and chemical reaction. Vaporization and chemical conversion are simulated for different ambient conditions. The competitive effects of sensible heating rate and the rate of vaporization with diffusion of cerium nitrate is seen to play a key role in determining the mass fraction of ceria formed within the droplet. Spatially resolved modeling of the droplet enables the understanding of the conversion of chemical species in more detail.

An analysis of MONTBLEX data on heat and momentum flux at Jodhpur

Parameterization of sensible heat and momentum fluxes as inferred from an analysis of tower observations archived during MONTBLEX-90 at Jodhpur is proposed, both in terms of standard exchange coefficients C-H and C-D respectively and also according to free convection scaling. Both coefficients increase rapidly at low winds (the latter more strongly) and with increasing instability. All the sensible heat flux data at Jodhpur (wind speed at 10m <(U)over bar (10)>, < 8ms(-1)) also obey free convection scaling, with the flux proportional to the '4/3' power of an appropriate temperature difference such as that between 1 and 30 m. Furthermore, for <(U)over bar (10)> < 4 ms(-1) the momentum flux displays a linear dependence on wind speed.

Unsteady flow and heat transfer between rotating coaxial disks

A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts on the rotating surfaces are obtained at different nondimensional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Flow and heat transfer in a stagnation-point flow over a stretching sheet with a magnetic field

The flow and heat transfer problem in the boundary layer induced by a continuous moving surface is important in many manufacturing processes in industry such as the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheet, the cooling of an infinite metalic plate in a cooling bath (which may also be electrolyte). Glass blowing, continuous casting and spinning of fibres also involve the flow due to a stretching surface. Sakiadis [1] was the first to study the flow induced by a semi-infinite moving wall in an ambient fluid. On the other hand, Crane [2] first studied the flow over a linearly stretching sheet in an ambient fluid. Subsequently, Crane [3] also investigated the corresponding heat transfer problem. Since then several authors [4-8] have studied various aspects of this problem such as the effects of mass transfer, variable wall temperature, constant heat flux, magnetic field etc. Recently, Andersson [9] has obtained an exact solution of the Navier-Stokes equations for the MHD flow over a linearly stretching sheet in an ambient fluid. Also Chiam [10] has studied the heat transfer with variable thermal conductivity on a stretching sheet when the velocities of the sheet and the free stream are equal.

Expression of the extracellular domain of the human heat-stable enterotoxin receptor in Escherichia coli and generation of neutralizing antibodies

The entire extracellular domain of the human heat-stable enterotoxin (ST) receptor as well as a truncated N-terminal domain were cloned as glutathione S-transferase fusion proteins and expressed in Escherichia coli. The recombinant fusion proteins were purified from both the cytosol and the inclusion body fractions by selective detergent extraction followed by glutathione-agarose affinity chromatography. The purified protein, corresponding to the entire extracellular domain, bound the stable toxin peptide with an affinity comparable to that of the native receptor characterized from the human colonic T84 cell line. No binding was observed with the N-terminal truncated fragment of the receptor under similar conditions, Polyclonal antibodies were raised to the entire extracellular domain fusion protein as well as the truncated extracellular domain fusion protein, and the antibodies were purified by affinity chromatography. Addition of the purified antibodies to T84 cells inhibited ST binding and abolished ST-mediated cGMP production, indicating that critical epitopes involved in ligand interaction are present in the N-terminal fragment of the receptor, Purified antibodies recognized a single protein of M(r) 160,000 Da on Western blotting with T84 membranes, corresponding to a size of the native glycosylated receptor in T84 cells. These studies are the first report of the expression, purification, and characterization of any member of the guanylyl cyclase family of receptors in E. coli and show that binding of the toxin to the extracellular domain of the receptor is possible in the absence of any posttranslational modifications such as glycosylation. The recombinant fusion proteins as well as the antibodies that we have generated could serve as useful tools in the identification of critical residues of the extracellular domain involved in ligand interaction.

Heat shock protein 70 on Neuro2a cells is a putative receptor for Japanese encephalitis virus

Japanese encephalitis virus (JEV) envelope (E) protein has been shown to play a critical role in attachment to cells. However, the receptor interacting with envelope protein has not been conclusively identified. Using mouse neuroblastoma (Neuro2a) cells and purified JEV-E protein in `Virus Overlay Protein Binding Assay' followed by MALDI-TOF analysis, we identified `heat shock protein 70' (Hsp70) as a possible receptor for JEV. Indirect immunofluorescence and flow-cytometry analysis demonstrated localization of Hsp70 on Neuro2a cell surface. Co-immunoprecipitation followed by Western blot analysis reconfirmed the interaction between Hsp70 and JEV-E protein. Further, anti-Hsp70 polyclonal-antibodies were able to block JEV entry into Neuro2a cells. Additionally, using the bioinformatic tool - FTDOCK, clocking between the proteins was performed. Amongst six interacting structural poses studied one pose involving RGD motif on JEV-E and leucine(539) on Hsp70 displayed stable interaction. These observations indicate that Hsp70 serves as putative receptor for JEV in Neuro2A cells.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.