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Nevertheless, for any finite N, no matter how large, this implies that the ground state has a restored O(2) symmetry. Implications for the finite-temperature phases, as well as the classical limit, of the HMF model are discussed.A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixed-node approximation. An imaginary-time propagator is derived rigorously from a discretized Hamiltonian, governing a non-Gaussian, sign-flipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginary-time resolutions and can be improved in a controlled manner. The method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015E_h of the exact basis-set-limit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10^-5E_h without an importance sampling or Jastrow factor.We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena, which are a hallmark of the irreversibility. By considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion. We also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time-dependent and steady-state simulations. This study is completed by calculating some critical exponents as function of the diffusion probability.The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it constantly produces entropy at the same time it extracts entropy out of the system. At steady state, the rate of entropy production e[over ̇]_p balances the rate of entropy extraction h[over ̇]_d. At equilibrium both entropy production and extraction rates become zero. The entropy production and entropy extraction rates are also sensitive to time. As time progresses, both entropy production and extraction rates increase in time and saturate to constant values. Nicotinamide Riboside mouse Moreover, employing microscopic stochastic approach, several thermodynamic relations for different model systems are explored analytically and via numerical simulations by considering a Brownian particle that moves in overdamped medium. Our analysis indicates that the results obtained for underdamped cases quantitatively agree with overdamped cases at steady state. The fluctuation theorem is also discussed.Diverse biological functions of biomembranes are made possible by their rich dynamic behaviors across multiple scales. While the potential coupling between the dynamics of differing scales may underlie the machineries regulating the biomembrane-involving processes, the mechanism and even the existence of this coupling remain an open question, despite the latter being taken for granted. Via inelastic neutron scattering, we examined dynamics across multiple scales for the lipid membranes whose dynamic behaviors were perturbed by configurational changes at two membrane regions. Surprisingly, the dynamic behavior of individual lipid molecules and their collective motions were not always coupled. This suggests that the expected causal relation between the dynamics of the differing hierarchical levels does not exist and that an apparent coupling can emerge by manipulating certain membrane configurations. The findings provide insight on biomembrane modeling and how cells might individually or concertedly control the multiscale membrane dynamics to regulate their functions.The first step in nonlinear time-series analysis can be selecting a delay for reconstruction. The most popular choices of this delay are the first zero of the autocovariance and the first minimum of the mutual information. An advantage of the first method arises from the robustness to noise of the autocovariance function, while an advantage of the second is that the first minimum of the mutual information provides a useful choice of delay for a wide range of nonlinear systems. We propose a method to choose a delay for frequently sampled flowlike data based on a mean local autocovariance function and compare its performance to methods based on the autocovariance and the mutual information. In addition, we compare the novel method to an established method based on cross-validatory mean-square errors of predictors corresponding to different choices of delay. The mean local autocovariance combines the versatility of the mutual information with some of the robustness to noise of the autocovariance.It has been discovered that active matter generates novel physical quantities such as the swim pressure. This quantity arises from the exchange of extra momentum between active particles and the boundaries of the system. Given its origin, this quantity can exist at different scales; hence microorganisms and larger organisms like fish or birds generate their own swim pressure. For larger organisms or for high swimming speeds, inertia cannot necessarily be neglected; hence in this paper, we start by calculating analytically the effect of finite translational and rotational particles' inertia on the diffusion of a system of noninteracting spherical active Brownian particles. From this analysis, an enhanced diffusion coefficient due to rotational inertia is obtained, and an alternative effective persistence length and an alternative reorientation time, both sensitive to rotational inertia, are also identified. Afterwards, and to see the implications of finite inertia on bulk properties, the pressure of this system is elucidated by calculating its respective swim and Reynolds pressures.
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