Kangrice3001

Emergence and collapse of coherent motions of self-propelled particles are affected more by particle motions and interactions than by their material or biological details. In the reconstructed systems of biofilaments and molecular motors, several types of collective motion including a global-order pattern emerge due to the alignment interaction. Meanwhile, earlier studies show that the alignment interaction of a binary collision of biofilaments is too weak to form the global order. The multiple collision is revealed to be important to achieve global order, but it is still unclear what kind of multifilament collision is actually involved. In this study, we demonstrate that not only alignment but also crossing of two filaments is essential to produce an effective multiple-particle interaction and the global order. We design the reconstructed system of biofilaments and molecular motors to vary a probability of the crossing of biofilaments on a collision and thus control the effect of volume exclusion. In this system, biofilaments glide along their polar strands on the turf of molecular motors and can align themselves nematically when they collide with each other. Our experiments show the counterintuitive result, in which the global order is achieved only when the crossing is allowed. When the crossing is prohibited, the cluster pattern emerges instead. We also investigate the numerical model in which we can change the strength of the volume exclusion effect and find that the global orientational order and clusters emerge with weak and strong volume exclusion effects, respectively. With those results and simple theory, we conclude that not only alignment but also finite crossing probability are necessary for the effective multiple-particles interaction forming the global order. Additionally, we describe the chiral symmetry breaking of a microtubule motion which causes a rotation of global alignment.The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g_2(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic "hyperuniform" varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms understanding of many-body physics. selleck inhibitor Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ν_a≈1/2 for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law τ_r∼Pe^-4/3 (Pe is Péclet number).Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical mechanical entropy is defined by Gibbs. The relation between these two definitions of entropy is still not fully explored. In this work, we study this problem by employing the phase-space formulation of quantum mechanics. For those quantum states having well-defined classical counterparts, we study the quantum-classical correspondence and quantum corrections of the entropy. We expand the von Neumann entropy in powers of ℏ by using the phase-space formulation, and the zeroth-order term reproduces the Gibbs entropy. We also obtain the explicit expression of the quantum corrections of the entropy. Moreover, we find that for the thermodynamic equilibrium state, all terms odd in ℏ are exactly zero. As an application, we derive quantum corrections for the net work extraction during a quantum Carnot cycle. Our results bring important insights into the understanding of quantum entropy and may have potential applications in the study of quantum heat engines.The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having N_x sites, the universal Casimir scaling function, which characterizes the leading finite-size correction term in the large-N_x expansion of the ground-state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime.We demonstrate that considerable variation of mean Prandtl number (Pr_0) from unity brings in an additional length scale (called the viscous penetration depth, δ_v) into the dynamics of instantaneous as well as time-averaged (mean) flow induced by thermoviscous expansion along a periodically heated solid wall. We investigate the limiting cases of high and low Prandtl numbers (Pr_0≫1 and Pr_0 ≪ 1) through detailed order-of-magnitude analysis. Our study reveals that the viscous penetration depth scales universally with Pr_0 so long as such depth remains small compared to the wavelength of the applied thermal wave. While a high Pr_0 is found to obstruct the mean flow, the converse is not necessarily true. Subsequent analysis clearly shows that a low-Pr_0 flow can induce negative thermoviscous force within the thermal boundary layer and thus retard the mean motion, leading to a nontrivial reduction of net mass flow along the plate. Numerical prediction of friction factor variation with Pr_0 agrees well with the scaling estimates for both high-Pr_0 and low-Pr_0 fluids.