We analyzed the effect of confinement on the effective diffusion of a run-and-tumble E. coli-like flagellated microswimmer. We used a simulation protocol where the run phases are obtained via a fully resolved swimming problem, i.e., Stokes equations for the fluid coupled with rigid-body dynamics for the microorganism, while tumbles and collisions with the walls are modeled as random reorientation of the microswimmer. For weak confinement, the swimmer is trapped in circular orbits close to the solid walls. In this case, optimal diffusivity is observed when the tumbling frequency is comparable with the angular velocity of the stable orbits. For strong confinement, stable circular orbits disappear and the diffusion coefficient monotonically decreases with the tumbling rate. Our findings are generic and can be potentially applied to other natural or artificial chiral microswimmers that follow circular trajectories close to an interface or in confined geometries.

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.

This paper presents a fundamental theory of nanobubble formation and induced force in confined nanochannels. It is shown that nanobubble formation between hydrophobic plates can be predicted from their surface tension and geometry, with estimated values for the surface free energy and the force acting on the plates in good agreement with the results of molecular dynamics simulation and experimentation. When a bubble is formed between two plates, vertical attractive force and horizontal retract force due to the shifted plates are applied to the plates. The net force exerted on the plates is not dependent on the distance between them. The short-range force between hydrophobic surfaces due to hydrophobic interaction appears to correspond to the force estimated by our theory. We compared between experimental and theoretical values for the binding energy of a molecular motor system to validate our theory. The tendency that the binding energy increases as the size of the protein increases is consistent with the theory.

The Enskog kinetic theory for moderately dense gas-solid suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the environmental fluid on solid particles is modeled via a viscous drag force plus a stochastic Langevin-like term. The Enskog equation is solved by means of two independent but complementary routes: (i) Grad's moment method and (ii) event-driven Langevin simulation of hard spheres. Both approaches clearly show that the flow curve (stress-strain rate relation) depends significantly on the volume fraction of the solid particles. In particular, as the density increases, there is a transition from the discontinuous shear thickening (observed in dilute gases) to the continuous shear thickening for denser systems. The comparison between theory and simulations indicates that while the theoretical predictions for the kinetic temperature agree well with simulations for densities $\phi \lesssim 0.5$, the agreement for the other rheological quantities (the viscosity, the stress ratio, and the normal stress differences) is limited to more moderate densities ($\phi \lesssim 0.3$) if the inelasticity during collisions between particles is not large.

Properties of helium atoms in the solid phase are investigated using the multiweight diffusion Monte Carlo method. Two different importance function transformations are used in two series of independent calculations. The kinetic energy is estimated for both the solid and liquid phases of ${}^4\mathrm{He}$. We estimate the melting and freezing densities, among other properties of interest. Our estimates are compared with experimental values. We discuss why walkers biased by two distinctly different guiding functions do not lead to noticeable changes in the reported results. Criticisms concerning the bias introduced into our estimates by population control and system size effects are considered.

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

A study of ice formation in stationary turbulent conditions is carried out in various limit regimes of crystal growth, supercooling, and ice entrainment at the water surface. Analytical expressions for the temperature, salinity, and ice concentration mean profiles are provided, and the role of fluctuations in ice production is numerically quantified. Lower bounds on the ratio of sensible heat flux to latent heat flux to the atmosphere are derived and their dependence on key parameters such as salt rejection in freezing and ice entrainment in the water column is elucidated.

Understanding the transport properties of charged particle beams is important not only from a fundamental point of view but also due to its relevance in a variety of applications. A theoretical model is established in this article, to model the interaction of a tenuous positively charged ion beam with an ultradense quantum electron-ion plasma, by employing a rigorous relativistic quantum-hydrodynamic (fluid plasma) electrostatic model proposed in McKerr et al. [M. McKerr, F. Haas, and I. Kourakis, Phys. Rev. E 90, 033112 (2014)]. A nonlinear analysis is carried out to elucidate the propagation characteristics and the existence conditions of large amplitude electrostatic solitary waves propagating in the plasma in the presence of the beam. Anticipating stationary profile excitations, a pseudomechanical energy balance formalism is adopted to reduce the fluid evolution equation to an ordinary differential equation. Exact solutions are thus obtained numerically, predicting localized excitations (pulses) for all of the plasma state variables, in response to an electrostatic potential disturbance. An ambipolar electric field form is also obtained. Thorough analysis of the reality conditions for all variables is undertaken in order to determine the range of allowed values for the solitonic pulse speed and how it varies as a function of the beam characteristics (beam velocity and density).

We study several aspects of the recently introduced fixed-phase spinor diffusion Monte Carlo method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure calculations. We illustrate constructions of spinor-based wave functions with the full space-spin symmetry without assigning up or down spin labels to particular electrons, effectively “complexifying” even ordinary real-valued wave functions for Hamiltonians without spin terms. Interestingly, with proper choice of the simulation parameters and spin variables, such fixed-phase calculations enable one to reach also the fixed-node limit. The fixed-phase approximation has several desirable properties when compared to the fixed-node approximation. The fixed-phase solution provides a straightforward interpretation as the lowest bosonic state in a given effective potential generated by the many-body approximate phase, whereas nodal boundary conditions are defined through less intuitive and complicated hypersurfaces with one dimension less than the original configuration space. In addition, the divergences of the local energy and drift at real wave function nodes are smoothed out to lower dimensionality when the wave function is complexified, thus decreasing the variation of sampled quantities and eliminating artificial nodal domain issues that can occur in the fixed-node formalism. We illustrate some of these properties on calculations of selected first-row systems that recover the fixed-node results with quantitatively similar levels of the corresponding biases. At the same time, the fixed-phase approach opens new possibilities for more general trial wave functions with further opportunities for increasing accuracy in practical calculations.

We explore the phase diagram of Ising spins on one-dimensional chains that criss-cross in two perpendicular directions and that are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian that has been proposed as a model of magnetic behavior in ${\mathrm{Nb}}_{12}{\mathrm{O}}_{29}$ and also, conceptually, as a geometry that is intermediate between one and two dimensions. Using mean-field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit, we demonstrate nontrivial critical behavior, including tricritical points that separate first- and second-order phase transitions. Finally, we present evidence that this model belongs to the two-dimensional Ising universality class.

Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ${\varphi }^4$ model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.

We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out-of-equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same nonexponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin recrossings and establishing the corresponding waiting time probability density function (PDF), $\psi \left(t\right)$. In the former case, with no crucial events, $\psi \left(t\right)$ is an exponential, and in the latter case, with crucial events, $\psi \left(t\right)$ is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes.

We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.

We present a method for the separation of superimposed, independent, autocorrelated components from noisy multichannel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account, and thereby increases the effective signal-to-noise ratio considerably, allowing separations even in the high-noise regime. Characteristics of the measurement instruments can be included, allowing for application in complex measurement situations. Independent posterior samples can be provided, permitting error estimates on all desired quantities. Using the concept of information field theory, the algorithm is not restricted to any dimensionality of the underlying space or discretization scheme thereof.

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension $D_u=4$. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the $d$-dimensional cross sections and the $d$-dimensional BTW model for $d=2$ and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops $d_f$, which is found to be $1.50\pm 0.02\approx \frac{3}{2}=d_f^{\text{GFF}}$.

We use invasion percolation to compute numerical values for bond and site percolation thresholds $p_c$ (existence of an infinite cluster) and $p_u$ (uniqueness of the infinite cluster) of tesselations $\{P,Q\}$ of the hyperbolic plane, where $Q$ faces meet at each vertex and each face is a $P$-gon. Our values are accurate to six or seven decimal places, allowing us to explore their functional dependency on $P$ and $Q$ and to numerically compute critical exponents. We also prove rigorous upper and lower bounds for $p_c$ and $p_u$ that can be used to find the scaling of both thresholds as a function of $P$ and $Q$.

A Boltzmann-like kinetic equation for a quasi-two-dimensional gas of hard spheres is derived. The system is confined between two parallel hard plates separated a distance between one and two particle diameters. An entropy Lyapunov function for the equation is identified. In addition to the usual Boltzmann expression, it contains a contribution associated to the confinement of the particles. The steady properties of the system agree with equilibrium statistical mechanics results. Equations describing the energy transfer between the degrees of freedom parallel and perpendicular to the confining plates are obtained for some simple initial configurations. The theoretical predictions are compared with molecular dynamics simulation data and a good agreement is found.

We investigate the distribution of potential and kinetic energy in stationary states of the linearly damped stochastic oscillator driven by Lévy noises. In the long time limit distributions of kinetic and potential energies of the oscillator follow the power-law asymptotics and do not fulfill the equipartition theorem. The partition of the mechanical energy is controlled by the damping coefficient. In the limit of vanishing damping a stochastic analog of the equipartition theorem can be proposed, namely, the statistical properties of potential and kinetic energies attain distributions characterized by the same widths. For larger damping coefficient the larger fraction of energy is stored in its potential form. In the limit of very strong damping the contribution of kinetic energy becomes negligible. Finally, we demonstrate that the ratio of instantaneous kinetic and potential energies, which signifies departure from the mechanical energy equipartition, follows universal power-law asymptotics, regardless of the symmetric $\alpha$-stable noise parameters. Altogether our investigations clearly indicate strongly nonequilibrium character of Lévy-stable fluctuations with the stability index $\alpha <2$.

A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change $\mathrm{\Delta }F$ of a system at inverse temperature $\beta$ from an ensemble average of nonequilibrium exponential work, i.e., $\langle e^{-\beta W}\rangle =e^{-\beta \mathrm{\Delta }F}$. The number of experimental work values needed to reach a given accuracy of $\mathrm{\Delta }F$ is determined by the variance of $e^{-\beta W}$, denoted $\mathrm{var}\left(e^{-\beta W}\right)$. We discover in this work that $\mathrm{var}\left(e^{-\beta W}\right)$ in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging $\mathrm{var}\left(e^{-\beta W}\right)$ at sufficiently low temperatures, markedly different from the classical behavior. The divergence of $\mathrm{var}\left(e^{-\beta W}\right)$ indicates the too-far-from-equilibrium nature of a nonadiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test the Jarzynski equality.