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We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics [ABSTRACT FROM AUTHOR]

An extended analysis of links between linear differential equations and the nonlinear Painlevé equation PV I is given. For linear equations, second-order equations in different forms, as well as various first-order systems, are chosen. The role of an accessory parameter is explained. The relationship to the Schlesinger system is made clear. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate that by using a mathematical physics approach--focusing attention on the physics and using mathematics as a tool--it is possible to visualize the formation of the transverse modes inside a cylindrical waveguide. The opposite (physical mathematics) approach looks at the mathematical problem and then tries to impose a physical interpretation. For cylindrical waveguides, the physical mathematics route leads to the Bessel differential equation, and it is argued that in the core of the waveguide there are only Bessel functions of the first kind in the description of the transverse modes. The Neumann functions are deemed non-physical due to their singularity at the origin and are eliminated from the final description of the solution. In this paper, by combining geometric optics and wave optics concepts, we show that the inclusion of the Neumann function is physically necessary to describe fully and properly the formation of the propagating transverse modes. With this approach, we also show that the field outside a dielectric waveguide arises in a natural way. [ABSTRACT FROM AUTHOR]

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ reversible Markov chains. Reversible chains obey detailed balance and thus ensure that the system will eventually relax to equilibrium, though detailed balance is not necessary for convergence to equilibrium. We review nonreversible Markov chains, which violate detailed balance and yet still relax to a given target stationary distribution. In particular cases, nonreversible Markov chains are substantially better at sampling than the conventional reversible Markov chains with up to a square root improvement in the convergence time to the steady state. One kind of nonreversible Markov chain is constructed from the reversible ones by enlarging the state space and by modifying and adding extra transition rates to create non-reversible moves. Because of the augmentation of the state space, such chains are often referred to as lifted Markov Chains. We illustrate the use of lifted Markov chains for efficient sampling on several examples. The examples include sampling on a ring, sampling on a torus, the Ising model on a complete graph, and the one-dimensional Ising model. We also provide a pseudocode implementation, review related work, and discuss the applicability of such methods. [ABSTRACT FROM AUTHOR]

The lattice parameters of monoclinic ortho-bromobenzophenone (2-BrBP) were determined using powder X-ray diffraction, in the temperature range of 90-300K. It is found that orthobromobenzophenone has small linear expansion coefficients (about 105 K-1) and is characterized by weak anisotropy. There were no phase transitions in the studied temperature range. [ABSTRACT FROM AUTHOR]

A numerical modeling method for accurately predicting the acoustophoretic motion of compressible microparticles in microfluidic devices is presented to consider the effects of fluid medium flow and spatial temperature variation that can significantly influence the acoustophoretic motion. In the proposed method, zeroth-order fluid medium flow and temperature, and first- and second-order acoustic fields in the microfluidic devices are first calculated by applying quadratic mapping functions and a second-order finite difference method (FDM) to perturbed mass, momentum, and energy conservation equations and state equation. Then, the acoustic radiation force is obtained based on the Gorkov's acoustic radiation force equation and applied to the Newton's Equation of Motion to calculate the microparticle motion. The proposed method was validated by comparing its results to a commercial software package, COMSOL Multiphysics results, one-dimensional, analytical modeling results, and experimental results. It is shown that the fluid medium flow affects the acoustic radiation force and streaming significantly, resulting in the acoustic radiation force and streaming prediction errors of 10.9% and 67.4%, respectively, when the fluid medium flow speed is increased from 0 to 1m/s. A local temperature elevation from 20 °C to 22°C also results in the prediction errors of 88.4% and 73.4%. [ABSTRACT FROM AUTHOR]

Https://tinyurl.com/WS-EKexp https://www.youtube.com/user/EugeneKhutoryansky/ Eugene K continues his development of excellent graphical animations and representations of applied mathematical physics, in this case an introduction to the simple exponential growth and decay equations. Graphs and vectors are animated alongside animated circuits and braking vehicles, and limitations to fitting these mathematical models to reality are mentioned. [Extracted from the article]

We have derived a family of equations related to the untwisted affine Lie algebras Ar(1) rusing a Coxeter Zr+1 reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. Applying additional Z2-involutions, we also obtain the real Hamiltonian forms of these equations. We also give some particular examples and impose additional reductions. [ABSTRACT FROM AUTHOR]

A method of active acoustic resonance interference spectroscopy is introduced for estimation of bubble properties. A modified form of Rayleigh-Plesset equation for forced oscillation of either a single free bubble or elastic shell encapsulated microbubble with attached solids loading is solved by the regular perturbation method for steady oscillatory solutions as a result of small amplitude acoustic excitation by a point sinusoidal oscillator. A model for the total pressure field at an acoustic receiver in an incompressible liquid is then solved by the regular perturbation method. Closed-form analytical solutions are found for pressure power at the acoustic receiver as a function of the excitation frequency and strength; the properties of the bubble, liquid, and encapsulating shell; and the geometry of the active monitoring system. The receiver pressure power exhibits a maximum due to bubble resonance and a minimum due to destructive interference between source and bubble response pressure fields at higher excitation frequencies. The inverse problem is solved to derive unique closed-form analytical estimators for bubble equilibrium size, attached solids mass loading, and encapsulating layer dilatational viscosity as a function of the frequencies of the fundamental resonance maximum, interference minimum, second harmonic maximum total average acoustic power, monitoring system, and phase properties. [ABSTRACT FROM AUTHOR]

We have derived a family of equations related to the untwisted affine Lie algebras Ar(1) rusing a Coxeter Zr+1 reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. Applying additional Z2-involutions, we also obtain the real Hamiltonian forms of these equations. We also give some particular examples and impose additional reductions. [ABSTRACT FROM AUTHOR]

The article focuses on showing physics problems through drawings, figures and sketches. Topics discussed include creating artistic drawings to solve physics problems, sketch of an illustration for problem types, sketch of semi open ended problem and evaluation problem and using various problems types to make students used to it.