The laws of establishing stationary composition in a droplet condensing in a binary vapor-gas environment

It is shown that the mole fractions of components within a droplet growing in an atmosphere of two condensing gases and a carrier gas approach their stationary values with a power-law behavior in time on a large scale and with exponential behavior on a small scale for both diffusion-controlled and free-molecular regimes of isothermal condensation. The parameters of the power and the exponential laws are specified for each regime of binary condensation and are linked to the thermodynamic and kinetic characteristics of condensing vapors and to the stationary mole fractions of the components in a growing binary droplet. The stationary composition of the solution within the droplet is shown to be established at a comparatively small relative increase of the droplet radius. A relaxation equation for the droplet composition at arbitrary initial deviations of mole fractions from their stationary values has been solved, and the limitations on the initial deviations allowing monotonic establishment of stationary composition in solution within a growing droplet have been considered.     

Fluctuation relations without microreversibility in nonlinear transport

In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. For nonlinear transport, there exist fluctuation relations that rely on Onsager's principle of microscopic reversibility away from equilibrium. However, both theory and experiments have shown deviations from microreversibility in the form of magnetic field asymmetric current-voltage relations. We present novel fluctuation relations for nonlinear transport in the presence of magnetic fields that relate current correlation functions at any order at equilibrium to response coefficients of current cumulants of lower order. We illustrate our results with the example of an electrical Mach-Zehnder interferometer.     

Current Symmetries for Particle Systems with Several Conservation Laws

We consider stochastic interacting particle systems with more than one conservation law in a regime far from equilibrium. Using time reversal we derive symmetry relations for the stationary currents of the conserved quantities that are reminiscent of Onsager’s reciprocity relations. These relations are valid for a very large class of particles with only some mild assumption on the decay of stationary relations and imply that the coarse-grained macroscopic dynamics is governed by a system of hyperbolic conservation laws. An explicit expression for the conserved Lax entropy is obtained.     

Separation characteristics of alcohol from aqueous solution by ultrasonic atomization

The generation rate of ultrasonically atomized droplets and the alcohol concentration in droplets were estimated by measuring the flow rate and the alcohol concentration of vapors from a bulk solution with a fountain. The effect of the alcohol concentration in the bulk solution on the generation rate of droplets and the alcohol concentration in droplets were investigated. The ultrasonic frequency was 2.4 MHz, and ethanol and methanol aqueous solutions were used as samples. The generation rate of droplets for ethanol was smaller than that for methanol at the same alcohol molar fraction in the bulk solution. For both solutions, at low alcohol concentration in the bulk solution, the alcohol concentration in droplets was lower than that in vapors and the atomized droplets were visible. On the other side, at high concentration, the concentration in droplets exceeded that in vapors and the atomized droplets became invisible. These results could be explained that the alcohol-rich clusters in the bulk solution were preferentially atomized by ultrasonic irradiation. The concentration in droplets for ethanol was higher than that for methanol at low alcohol concentration because the amount of alcohol-rich clusters was larger. When the alcohol molar fraction was greater than 0.6, the atomized droplets almost consisted of pure alcohol.     

Perturbation Expansion Method and Effective Medium Approximation for Effective Conductivity of Nonlinear Composite Media

In this paper, we establish an effective medium approximation (EMA) for effective conductivity of nonlinear composite media. As an example, we consider a two-dimensional composite medium with a cylindrical inclusion embedded in a homogeneous host, both the host and the inclusion having nonlinear current-voltage constitutive relations, and apply the perturbation expansion method to derive its analytic series solution. Using the nonlinear EMA we derive the formulae of the first, the third and the fifth-order effective conductivities, which are valid for nonlinear composite media with middle concentration of inclusion.     

Boiling-up of superheated water and water solutions under ultrasound influence

Boiling-up kinetics of superheated distilled water and sodium chloride solution in a glass cell at atmospheric pressure and low superheating of 15–35 °C has been studied far from the boundary of attainable superheating in the area of heterogeneous nucleation. Temperature dependences of average waiting time of superheated liquids boiling-up have been studied experimentally under natural conditions and in the ultrasonic field Waiting time of boiling-up at these temperatures reaches 1000 s, and average time is 600 s. Empirical distribution functions have been found with the use of the waiting time samples obtained by the method of order statistics. Omega-square goodness-of-fit test has shown that they disagree with exponential distribution describing stationary random process of supercritical embryo generation separating the system to macroscopic phases. Thus, it is shown that this random process is not stationary, consequently, nucleation rate to be depending on time.     

Exact solutions of discrete master equations in terms of continued fractions

We present the continued fraction solution for the stationary probability of discrete master equations of one-variable processes. After we elucidate the method for simple birth and death processes we focus the study on processes which introduce at least two-particle jumps. Consequently, these processes do in general not obey a detailed balance condition. The outlined method applies as well to solutions of eigenmodes of the stochastic operator. Further we derive explicit continued fraction solutions for the Laplace transform of conditional probabilities. All the various continued fraction coefficients are given directly in terms of the transition rates and they obey recursion relations. The method is illustrated for the stationary solution of a simple nonlinear chemical reaction scheme originated by Nicolis.     

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.     

Interaction of electromagnetic waves with nonlinear substance layer under conditions of electron paramagnetic resonance in millimeter waves

Trancated equations have been obtained by the Green's functions method for a slowly varying amplitude of a transverse magnetic field component in a paramagnetic layer under conditions of the electron paramagnetic resonance (EPR). A magnetic susceptibiliti of the substence has been found from the Bloch equation for a homogeneously line breadth of the EPR. In a stationary case a solution of a nonlinear boundary-value problem is redused to a solution of two boundary problems for amplitude and phase equations. It is shown that unstable regimes of the electrodynamic system under inves tigation are possible.Electrodynamic characteristics of a nonlinear resonator of the Fabry-Pero type filled with a saturated paramagnetic medium have been analyzed numerically in a non-stationery case.     

Stochastic theory of nonlinear rate processes with multiple stationary states. II. Relaxation time from a metastable state

We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Study of the reciprocity relations for a nonlinear multipole in inhomogeneous magnetic field

The reciprocity relations for a matrix of nonlinear resistances of a multipole placed in an inhomogeneous magnetic field are obtained based on the material equation of a nonlinear inhomogeneous nonstationary conducting medium in the Landau collision integral approximation. The question about the measured potentials of the multipole terminals in the quasi-stationary mode is discussed. A method for testing the obtained reciprocity relations has been proposed and the experimental data have been presented. It has been shown that the reciprocity relations are valid for a nonlinear multipole within the electric measurement error.     

Thermal diffusion in a sinusoidal temperature field

Separation of liquid mixtures in a thermal gradient, known as the Ludwig-Soret effect or thermal diffusion, is governed by a nonlinear, partial differential equation. It is shown here that the nonlinear differential equation for a binary mixture can be reduced to a Hamiltonian system of equations and that a solution can be obtained for the linear problem. The calculation gives a closed form expression for the space and time dependence of the concentration profile of the mixture, valid at short times.     

The category of Fresnel kernels

Symplectic relations and their generating functions have found extensive applications in classical mechanics. In the present paper we undertake the study of the correspondence between generating functions of symplectic relations and kernels of integral operators of quantum theories. As a first step we study this correspondence in the case of linear symplectic relations generated by quadratic functions. The theory is sufficiently complicated even in this simple case. Additional complications must be expected in the general nonlinear theory due to the fact that the composition of regular nonlinear symplectic relations is in general singular and that nonlinear symplectic relations in general do not have global generating functions. The present paper is a continuation of the study of linear symplectic relations undertaken in [2].     

Stationary Fokker-Planck equation applied to fission dynamics

By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus ¹⁶⁸Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus ²¹³At.     

Effect of the stagnation temperature on supersonic flow parameters: Application for air in nozzles

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect and its state equation always remains valid, except it will be called a calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios and to study the supersonic flow at high temperature (lower than the threshold of dissociation). The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm is used for the numerical integration of the found integrals. A condensation of the nodes is used, since the functions to be integrated have a high gradient at the extremity of the interval of integration. A comparison is made with a calorifcally perfect gas to determine the error of this. An application is made for air in a supersonic nozzle. The text was submitted by the authors in English.     

Studies of the Longitudinal Electrophoresis Dynamics in Pulse-Periodic Discharges

The establishing in time of the axial distribution of metal vapors is studied on injecting them electrophoretically into a pulse-periodic discharge. In particular, the time-dependent solution of the diffusion equation for the metal vapor concentration is obtained averaged through a number of pulses. The axial distributions of vapors for various instants of time are calculated. The homogeneity criteria for these distributions are determined. The settling times of the homogeneous distribution in conditions typical for the pulse-periodic metal vapor lasers are found. These times are rather short (about 1 s). The results obtained show promise for using electrophoresis in pulse-periodic metal vapor lasers to form homogeneous active media.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

Solvatochromic and nonlinear optical properties of Eosin B in solvents and AOT/water/Heptane

The third-order susceptibility and second-order hyperpolarizability and the two-photon absorption coefficient of Eosin-B in AOT/water/Heptane were investigated by using the Z-Scan technique. The droplets were prepared with an AOT/water droplet in a continuous phase of Heptane. The droplets size changes with the amount of water and the droplet concentration decreases with the increase of Heptane concentration. To study the nonlinear optical properties of Eosin-B, the Z-scan measurements were performed by means of a laser at 532 nm and 80 mW power. The nonlinear refractive and the nonlinear absorption coefficient indices were found to be in the order of 10^?12 (cm² W^?1) and 10^?7 (cm W^?1), respectively. The change of nonlinear optical properties of Eosin-B by droplet size and concentration is due to the change of dye aggregation and thermal conductivity and thermo-optic coefficient of samples. The absorption of Eosin-B changes with the polarity of the medium (dielectric constant and refractive index). It has been shown that the intensity of emission spectra of Eosin-B in AOT/water/Heptane is enhanced compared to that of aqueous solution. By the Bilot and Kawski theory, the ratio between the excited state and the ground state of the dipole moments (μ_e/μ_g) of Eosin-B both in water and in droplets is extracted.     

On the thermodynamic size limit of nanowires grown by the vapor-liquid-solid process

For nanowires grown by the vapor-liquid-solid (VLS) process, expressions of the thermodynamically allowed minimum sizes of the nanowire and the liquid phase droplet as functions of the relevant thermodynamic variables have been obtained using Si nanowires (SiNW) grown from metal-silicon (M-Si) systems as the model case. In these expressions the binary nature of the M-Si system, which involves four phases of materials, is accounted for. The liquid droplet minimum size is determined by a unique set of the external M and Si vapor phase pressure values. The SiNW minimum size expression contains two contributions, one due to the liquid droplet composition and one due to the droplet size. These expressions do not predict a limit on the attainable VLS SiNW minimum size, implying ever smaller SiNW can be grown until reaching some growth kinetic limit which is presently unknown. A set of size data of the smallest experimentally grown SiNW appears to have approached an effective limit set by the liquid composition. PACS 81.07b; 61.46+w; 61.25Mv