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.

Intraseasonal Variation of the Summer Monsoon I:Observational Aspects

Within the summer monsoon, the circulation and rainfall over the Indian region exhibit large variations over the synoptic scale of 3-7 days and the supersynoptic scales of 10 days and longer. In this paper we discuss some facets of intraseasonal variation on the supersynoptic scale on the basis of existing observational studies and some new analysis. The major variation of the summer monsoon rainfall on this scale is the active-break cycle. The deep convection over the Indian region on a typical day in the active phase is organized over thousands of kilometers in the zonal direction and is associated with a tropical convergence zone (TCZ). The intraseasonal variations on the supersynoptic scale are also coherent on these scales and are related to the space-time variation of the large-scale TCZ. The latitudinal distribution of the occurrence of the TCZ is bimodal with the primary mode over the heated continent and a secondary mode over the ocean. The variation of the continental TCZ is generally out of phase with that of the oceanic TCZ. During the active spells, the TCZ persists over the continent in the monsoon zone. The revival from breaks occurs either by northward propagation of the TCZ over the equatorial Indian Ocean or by genesis of a disturbance in the monsoon zone (often as a result of westward propagations from W. Pacific). The mechanisms governing the fluctuation between active spells and breaks, the interphase transition and the complex interactions of the TCZ over the Indian subcontinent with the TCZ over the equatorial Indian Ocean and the W. Pacific, have yet to be completely understood.

Pyroelectric and Electrostrictive Properties of (1 –x–y) PZN ·xBT ·yPT Ceramic Solid Solutions

The pyroelectric and electrostrictive properties of lead zinc niobate-lead titanate-barium titanate (PZN-BT-PT) ceramic solid solution were investigated. These properties of the (1 - x)PZN.xBT series were qualitatively explained with a composition fluctuation model. The pyroelectric depolarization temperatures of (1 - x - y)PZN.xBT.yPT ceramics were utilized to select compositions for room-temperature electrostrictive applications. Among them, 0.85PZN.0.10BT.0.05PT ceramic with Q11 = 0.018 m4/C2, Q12 = -0.0085 m4/C2, S2 at 25 kV/cm = -6.1 x 10(-4), T(max) = 75-degrees-C at 1 kHz, and T(t) = 27-degrees-C shows optimum properties for micropositioner applications.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Degradation and Failure of Field Emitting Carbon Nanotube Arrays

It has been observed experimentally that the collective field emission from an array of Carbon Nanotubes (CNTs) exhibits fluctuation and degradation, and produces thermal spikes, resulting in electro-mechanical fatigue and failure of CNTs. Based on a new coupled multiphysics model incorporating the electron-phonon transport and thermo-electrically activated breakdown, a novel method for estimating accurately the lifetime of CNT arrays has been developed in this paper. The main results are discussed for CNT arrays during the field emission process. It is shown that the time-to-failure of CNT arrays increases with the decrease in the angle of tip orientation. This observation has important ramifications for such areas as biomedical X-ray devices using patterned films of CNTs.

Inverse surface melting in confined clusters: Ar-13 in zeolite L

Monte Carlo and molecular dynamics simulations on an Ar-13 cluster in zeolite L have been carried out at a series of temperatures to understand the rigid-nonrigid transition corresponding to the solid-liquid transition exhibited by the free Ar-13 cluster. The icosahedral geometry of the free cluster is no longer preferred when the cluster is confined in the zeolite. The root-mean-squared pair distance fluctuation, delta, exhibits a sharp, well-defined rigid-nonrigid transition at 17 K as compared to 27 K for the free cluster. Multiple peaks in the distribution of short-time averages of the guest-host interaction energy indicate coexistence of two phases.; It is shown that this transition is associated with the inner atoms becoming mobile at 17 K even while the outer layer atoms, which are in close proximity to the zeolitic wall, continue to be comparatively immobile. This may be contrasted with the melting of large free clusters of 40 or more atoms which exhibit surface melting. Guest-host interactions seem to play a predominant role in determining the properties of confined clusters. We demonstrate that the volume of the cluster increases rather sharply at 17 and 27 K respectively for the confined and the free cluster. Power spectra suggest that the motion of the inner atoms is generally parallel to the atoms which form the cage wall.

Nonequilibrium phase transition in the kinetic Ising model: Divergences of fluctuations and responses near the transition point

The nonequilibrium dynamic phase transition in the kinetic Ising model in the presence of an oscillating magnetic field is studied by Monte Carlo simulation. The fluctuation of the dynamic older parameter is studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined ''susceptibility'' is also studied near the dynamic transition point. Similarly, the fluctuation of energy and appropriately defined ''specific heat'' is studied as a function of temperature near the dynamic transition point. In both cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (in power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).

Irreversibility-to-reversibility crossover in transient response of an optically trapped particle

We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system's time evolution shows dramatically different behaviors. Starting from the short-time reversible to long-time irreversible transition, a stationary reversible state with zero net dissipation can be achieved as the release point energy is decreased. If the system starts with even lower energy, it progressively extracts useful work from thermal noise and exhibits an anomalous irreversibility. In addition, we have verified the Transient Fluctuation Theorem and the Integrated Transient Fluctuation Theorem even for the non-ergodic descriptions of our system. Copyright (C) EPLA, 2011

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term , based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures.

Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis

Scattering of coherent light from scattering particles causes phase shift to the scattered light. The interference of unscattered and scattered light causes the formation of speckles. When the scattering particles, under the influence of an ultrasound (US) pressure wave, vibrate, the phase shift fluctuates, thereby causing fluctuation in speckle intensity. We use the laser speckle contrast analysis (LSCA) to reconstruct a map of the elastic property (Young's modulus) of soft tissue-mimicking phantom. The displacement of the scatters is inversely related to the Young's modulus of the medium. The elastic properties of soft biological tissues vary, many fold with malignancy. The experimental results show that laser speckle contrast (LSC) is very sensitive to the pathological changes in a soft tissue medium. The experiments are carried out on a phantom with two cylindrical inclusions of sizes 6 mm in diameter, separated by 8 mm between them. Three samples are made. One inclusion has Young's modulus E of 40 kPa. The second inclusion has either a Young's modulus E of 20 kPa, or scattering coefficient of mu'(s), = 3.00 mm(-1) or absorption coefficient of mu(a) = 0.03 mm(-1). The optical absorption (mu(a)), reduced scattering (mu'(s)) coefficient, and the Young's modulus of the background are mu(a) = 0.01 mm(-1), mu'(s) = 1.00 mm(-1) and 12kPa, respectively. The experiments are carried out on all three phantoms. On a phantom with two inclusions of Young's modulus of 20 and 40 kPa, the measured relative speckle image contrasts are 36.55% and 63.72%, respectively. Experiments are repeated on phantoms with inclusions of mu(a) = 0.03 mm-1, E = 40 kPa and mu'(s) = 3.00 mm(-1). The results show that it is possible to detect inclusions with contrasts in optical absorption, optical scattering, and Young's modulus. Studies of the variation of laser speckle contrast with ultrasound driving force for various values of mu(a), mu'(s), and Young's modulus of the tissue mimicking medium are also carried out. (C) 2011 American Institute of Physics. doi:10.1063/1.3592352]

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation.

Field emission properties of carbon nanotube arrays with defects and impurities

Field emission from carbon nanotubes (CNTs) in the form of arrays or thin films give rise to several strongly correlated process of electromechanical interaction and degradation. Such processes are mainly due to (1) electron-phonon interaction (2) electromechanical force field leading to stretching of CNTs (3) ballistic transport induced thermal spikes, coupled with high dynamic stress, leading to degradation of emission performance at the device scale. Fairly detailed physics based models of CNTs considering the aspects (1) and (2) above have already been developed by these authors, and numerical results indicate good agreement with experimental results. What is missing in such a system level modeling approach is the incorporation of structural defects and vacancies or charge impurities. This is a practical and important problem due to the fact that degradation of field emission performance is indeed observed in experimental I-V curves. What is not clear from these experiments is whether such degradation in the I-V response is due to dynamic reorientation of the CNTs or due to the defects or due to both of these effects combined. Non-equilibrium Green’s function based simulations using a tight-binding Hamiltonian for single CNT segment show up the localization of carrier density at various locations of the CNTs. About 11% decrease in the drive current with steady difference in the drain current in the range of 0.2-0.4V of the gate voltage was reported in literature when negative charge impurity was introduced at various locations of the CNT over a length of ~20nm. In the context of field emission from CNT tips, a simplistic estimate of defects have been introduced by a correction factor in the Fowler-Nordheim formulae. However, a more detailed physics based treatment is required, while at the same time the device-scale simulation is necessary. The novelty of our present approach is the following. We employ a concept of effective stiffness degradation for segments of CNTs, which is due to structural defects, and subsequently, we incorporate the vacancy defects and charge impurity effects in the Green’s function based approach. Field emission induced current-voltage characteristics of a vertically aligned CNT array on a Cu-Cr substrate is then simulated using a detailed nonlinear mechanistic model of CNTs coupled with quantum hydrodynamics. An array of 10 vertically aligned and each 12 m long CNTs is considered for the device scale analysis. Defect regions are introduced randomly over the CNT length. The result shows the decrease in the longitudinal strain due to defects. Contrary to the expected influence of purely mechanical degradation, this result indicates that the charge impurity and hence weaker transport can lead to a different electromechanical force field, which ultimately can reduce the strain. However, there could be significant fluctuation in such strain field due to electron-phonon coupling. The effect of such fluctuations (with defects) is clearly evident in the field emission current history. The average current also decreases significantly due to such defects.