Electric circuits influenced by thermal noise are analogous to confined Brownian particles and can be an alternative and convenient scheme for studying stochastic thermodynamics. Here we experimentally demonstrate an effective technique of generating tunable potentials for Brownian dynamics in an electric circuit, realized by external controlled feedback. We present two illustrative examples of one-dimensional virtual potentials static harmonic potential and time-varying double-well potential. The thermal noises of both cases undergo equivalent Brownian dynamics as if they were in the authentic potentials as long as the feedback is fast enough to respond to the designed potentials. The results show that the electric circuit provides a simple, effective, and programmable scheme to study the feedback-controlled virtual potential.It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation techniques that call for rigorous results against which they can be tested. In this context, the simplest case of high-dimensional linear regression has acquired significant new relevance and attention. In this paper we use the statistical physics perspective on inference to derive several exact results for linear regression in the high-dimensional regime.Wave-packet simulations, regarded as phonon dynamics in the literature, have been used to explore interface conductance problems and to study the frequency-based dynamics of systems of particles. In this work we introduce an extension of the method to improve the postsimulation analysis and to add an energy aspect to the definition of a wave packet. In a wave-packet simulation the most populated frequency activated with the wave packet is known through knowledge of the wave number implemented in the atom displacement equation. The one-to-one correspondence of wave number and frequency is known through the phonon dispersion relation (PDR). We add the temperature dependence of this one-to-one correspondence to the analysis of wave packets through consideration of a temperature-dependent PDR and showed the importance of the temperature-dependent PDR in the wave-packet definition by presenting results considering and neglecting the phenomenon. In addition, the temperature-dependent PDR and the density of states provide us the chance to change the nature of the atomic displacement amplitude as an arbitrary parameter to a tuning knob for the amount of energy it carries and utilize the chance to provide a quantitative measure for the validity of molecular-dynamics simulations considering their classical nature in comparison with the quantum particle picture of phonons.The Peierls-Nabarro barrier is a discrete effect that frequently occurs in discrete nonlinear systems. A signature of the barrier is the slowing and eventual stopping of discrete solitary waves. This work examines intense electromagnetic waves propagating through a periodic honeycomb lattice of helically driven waveguides, which serves as a paradigmatic Floquet topological insulator. Here it is shown that discrete topologically protected edge modes do not suffer from the typical slowdown associated with the Peierls-Nabarro barrier. Instead, as a result of their topological nature, the modes always move forward and redistribute their energy a narrow (discrete) mode transforms into a wide effectively continuous mode. On the other hand, a discrete edge mode that is not topologically protected does eventually slow down and stop propagating. Topological modes that are initially narrow naturally tend to wide envelope states that are described by a generalized nonlinear Schrödinger equation. These results provide insight into the nature of nonlinear topological insulators and their application.Establishing formal mathematical analogies between disparate physical systems can be a powerful tool, allowing for the well studied behavior of one system to be directly translated into predictions about the behavior of another that may be harder to probe. In this paper we lay the foundation for such an analogy between the macroscale electrodynamics of simple magnetic circuits and the microscale chemical kinetics of transcriptional regulation in cells. By artificially allowing the inductor coils of the former to elastically expand under the action of their Lorentz pressure, we introduce nonlinearities into the system that we interpret through the lens of our analogy as a schematic model for the impact of crosstalk on the rates of gene expression near steady state. Synthetic plasmids introduced into a cell must compete for a finite pool of metabolic and enzymatic resources against a maelstrom of crisscrossing biological processes, and our theory makes sensible predictions about how this noisy background might impact the expression profiles of synthetic constructs without explicitly modeling the kinetics of numerous interconnected regulatory interactions. We conclude the paper with a discussion of how our theory might be expanded to a broader class of plasmid circuits and how our predictions might be tested experimentally.In a recent paper Das et al. [J. Chem. Phys. 147, 164102 (2017)JCPSA60021-960610.1063/1.4999408] proposed the Fokker-Planck equation (FPE) for the Brownian harmonic oscillator in the presence of a magnetic field and the non-Markovian thermal bath, respectively. This system has been studied very recently by Hidalgo-Gonzalez and Jiménez-Aquino [Phys. Rev. E 100, 062102 (2019)PREHBM2470-004510.1103/PhysRevE.100.062102] and the Fokker-Planck equation was derived using the characteristic function. It includes a few extra terms in the FPE and the authors conclude that their method is accurate compared to the calculation by Das et al. Then we reexamine our calculation and which is present in this comment. https://www.selleckchem.com/products/ABT-888.html The revised calculation shows that both methods give the same result.The properties of freestanding tensionless interfaces and membranes at low bending rigidity κ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes Below the collapse transition κ_BP it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity κ_c the conformational correlation function are characterized by power-law behavior with a continuously varying exponent α, 2 less then α≤4 and above κ_c, α=4 characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to κ_c. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.