In this work we propose to identify the relative role of the inclination of gravitational acceleration and friction on the discharge flow rate of a granular media from a rectangular silo by varying the silo geometry thanks to an inclined bottom which ends up at a lateral outlet. The study is motivated by a nuclear safety problem: a fuel rod (modeled by an elongated silo) accidentally releases fuel fragments (modeled by grains). We performed experiments where we independently measured the mass flow rate and the velocity profiles, together with discrete particle simulations and continuum simulations with a frictional rheology described by a $\mu \left(I\right)$ constitutive law and taking into account the wall friction. We study monolayer flows and three-dimensional flows, and we propose an analytical model that predicts the discharge flow rate of particles from a rectangular silo with an inclined bottom according to its outlet aspect ratio and the bottom inclination angle.

Kinetic rates for thermochemical nonequilibrium models are generally computed from quasiclassical trajectory (QCT) calculations on accurate ab initio potential energy surfaces (PES). In this article, we use a feed-forward artificial neural network (ANN) to fit existing single-point energies for ${\mathrm{N}}_2+{\mathrm{N}}_2$ interactions [Bender et al., J. Chem. Phys. 143, 054304 (2015)] to construct a PES suitable for molecular simulation of high-temperature gas flows. We then perform detailed comparisons with a widely used ${\mathrm{N}}_4$ PES that was built using the permutation invariant polynomials (PIP) method. Specific physical considerations in the construction of the ANN for this application are detailed. Translation, rotation, and permutation invariance are precisely satisfied by mapping the interatomic distances onto a set of permutation invariant inputs, known as fundamental invariants (FI) that generate the permutation invariant polynomial ring. The diatomic energy is imposed by decomposing the total potential energy into a sum of a two-body and a many-body energy contribution. To obtain the correct dynamical behavior with the most basic, yet computationally efficient ANN, spurious long-distance interactions must be removed to avoid incorrect physical behavior at the dissociation threshold. We use a simple apodization function to smoothly taper off to zero any residual many-body interaction at large separations. Both accuracy and performance of the FI-ANN PES are assessed. QCT calculations are used to compute dissociation probabilities and vibrational energy distributions at various equilibrium temperatures. Excellent agreement with the results obtained from the PIP PES is found. For our test case, the ANN PES is also significantly more computationally efficient than the PIP PES at comparable root-mean-square error levels.

Quantum devices are systems that can explore quantum phenomena, such as entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as the main element in their high performance in powerful charging. In this paper, we explore quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two- and three-cell battery, our results suggest that entanglement is not the main resource in quantum batteries, where there is a nontrivial correlation-coherence tradeoff as a resource for the high efficiency of such quantum devices.

Finite-$N$ effects unavoidably drive the long-term evolution of long-range interacting $N$-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by $1/N$ effects but this kinetic operator exactly vanishes by symmetry for one-dimensional homogeneous systems: such systems undergo a kinetic blocking and cannot relax as a whole at this order in $1/N$. It is therefore only through the much weaker $1/N^2$ effects, sourced by three-body correlations, that these systems can relax, leading to a much slower evolution. In the limit where collective effects can be neglected, but for an arbitrary pairwise interaction potential, we derive a closed and explicit kinetic equation describing this very long-term evolution. We show how this kinetic equation satisfies an $H$-theorem while conserving particle number and energy, ensuring the unavoidable relaxation of the system toward the Boltzmann equilibrium distribution. Provided that the interaction is long-range, we also show how this equation cannot suffer from further kinetic blocking, i.e., the $1/N^2$ dynamics is always effective. Finally, we illustrate how this equation quantitatively matches measurements from direct $N$-body simulations.

We investigate the critical behavior of the modified Kuramoto model with an asymmetric dynamic interaction which has been proposed to explain the difference between the synchronized frequency and the average intrinsic frequency. We find that the discontinuous phase transition arises when oscillators interact only with other oscillators whose phases are ahead. From the comparison with the conventional Kuramoto model in which the interaction possesses phase reflection symmetry, we conclude that the dynamical symmetry breaking and the dynamic change in interaction structure play important roles in changing the transition nature from continuous to discontinuous ones.

The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a time delay between when unreliable environmental cues are sensed and when organisms can mount a response has yet to be explored at any length. Accounting for this delay in phenotype response in models of population growth, we find that a critical error probability can exist under certain environmental conditions: An organism with a sensory system with any error probability less than the critical value can achieve the same long-term growth rate as an organism with a perfect sensing system. We also observe a tradeoff between the evolutionary value of sensory information and robustness to error, mediated by the rate at which the phenotype distribution relaxes to steady state. The existence of the critical error probability could have several important evolutionary consequences, primarily that sensory systems operating at the nonzero critical error probability may be evolutionarily optimal.

The unequivocal role of electrostatic forces in biological (and colloidal) systems underscores the importance of attaining accurate and rapid calculations of electrostatic forces if one wishes to faithfully simulate the electrostatic aspect of a biological system. This paper makes significant progress toward this aspect as it rigorously incorporates ionic screening at the Debye-Hückel level for an electrolyte system containing dielectric spheres of finite radii. We investigated earlier this system without mobile ions via a surface charge method. However, the need for computing a large number of Wigner rotation matrix elements per configuration can significantly slow down the numerical calculations. This difficulty was recently overcome by our Wigner-matrix-free formalism. Unfortunately, in that method ions can only be included individually, making it impractical to investigate, for example, ionic screening in a system modeled by charged dielectric spheres immersed in a solution of mobile ions. Here, we overcome this difficulty by extending the surface charge method to treat ions implicitly. Previous treatments of charged dielectric spheres in a solution of mobile ions did not emphasize the energy reciprocity of electrostatics and are largely limited to a few spheres and/or special symmetries. Our new formalism respects reciprocity and accommodates arbitrarily many dielectric spheres of different dielectric constants and sizes while being rigorous at the Debye-Hückel level. The differences, and the relationship, between our new implicit ion treatment and our previous ion-free (or explicit ion) approach are described. A closed form for the electrostatic energy with implicit ions is also provided. This new formalism speeds up the computation of the electrostatic energy in the presence of ions, and accommodates permanent and induced multipoles that are very important when the polarization effect needs to be correctly included. We also mention how the proposed method can be transformed to a numerical method for use with arbitrary nonspherical surfaces.

We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. Upon surfactant application, the outer droplet deformation increases and the inner droplet deformation decreases. The concentrated surfactants on the outer interface increase deformation, and the inner droplet is affected by the inner flow. At a fixed Péclet number (Pe), the surfactant concentration at the outer interface increases with an increase in capillary number (Ca); however, such a tendency is difficult to identify at the inner interface. Next, the Pe effects are analyzed. With an increase in Pe, the deformation of the inner droplet decreases significantly. The local distribution of the surfactant considerably affects the double emulsion stabilization, which is analyzed in terms of internal flow. The interfacial tension gradient induced by the surfactant generates vortices internally, which is verified by applying the surfactant to each interface independently. The radius ratio affects droplet deformation and surfactant transport. The compression of the inner flow region increases the viscous force and decreases the interface velocity. Therefore, with an increase in radius ratio, the deformation increases, and the surfactant transport becomes slow.

In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson-Nernst-Planck equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain $S$-shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the $S$-shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the $S$-shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis transition dynamics, from a steady-state solution on the unstable branch to one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.

We study noncanonical relaxation in an aggregate of subsystems with negative specific heat. The Thirring instability drives the constituent subsystems towards the edges of their energy spectrum, so that the existence of a single adiabatic invariant results in structured noncanonical steady states that are spectacularly different from the grand-canonical prediction. For parameter regimes where this adiabatic invariance breaks down, the system exhibits prethermalization far away from integrability, with an unprecedented contrast between the prethermal- and thermal states.

We study the stochastic block model, which is often used to model community structures and study community-detection algorithms. We consider the case of two blocks in regard to its largest connected component and largest biconnected component, respectively. We are especially interested in the distributions of their sizes including the tails down to probabilities smaller than ${10}^{-800}$. For this purpose we use sophisticated Markov chain Monte Carlo simulations to sample graphs from the stochastic block model ensemble. We use these data to study the large-deviation rate function and conjecture that the large-deviation principle holds. Further we compare the distribution to the well-known Erdős-Rényi ensemble, where we notice subtle differences at and above the percolation threshold.

We present an action that can be used to study variationally the collapse of Bose-Einstein condensates. This action is real, even though it includes dissipative terms. It adopts long-range interactions between the atoms, so that there is always a stable minimum of the energy, even if the remaining number of atoms is above the number that in the case of local interactions is the critical one. The proposed action incorporates the time needed for the abrupt and delayed onset of collapse, yielding in fact its dependence on the scattering length. We show that the evolution of the condensate is equivalent to the motion of a particle in an effective potential. The particle begins its motion far from the point of stable equilibrium and it then proceeds to oscillate about that point. We prove that the resulting large oscillations in the shape of the wave function after the collapse have frequencies equal to twice the frequencies of the traps. Our results agree with the experimental observations.

We present a mechanical analog of a quantum wave-particle duality: a vibrating string threaded through a freely moving bead or “masslet.” For small string amplitudes, the particle movement is governed by a set of nonlinear dynamical equations that couple the wave field to the masslet dynamics. Under specific conditions, the particle achieves a regime of transparency in which the field and the particle's dynamics appear decoupled. In that special case, the particle conserves its momentum and a guiding wave obeying a Klein-Gordon equation, with real or imaginary mass, emerges. Similar to the double-solution theory of de Broglie, this guiding wave is locked in phase with a modulating group wave comoving with the particle. Interestingly, both subsonic and supersonic particles can fall into a quantum regime as is the case with the slower-than-light bradyons and hypothetical, faster-than-light tachyons of particle physics.

Many biological functions rely on the reshaping of cell membranes, in particular into nanotubes, which are covered in vivo by dynamic actin networks. Nanotubes are subject to thermal fluctuations, but the effect of these on cell functions is unknown. Here, we form nanotubes from liposomes using an optically trapped bead adhering to the liposome membrane. From the power spectral density of this bead, we study the nanotube fluctuations in the range of membrane tensions measured in vivo. We show that an actin sleeve covering the nanotube damps its high-frequency fluctuations because of the network viscoelasticity. Our work paves the way for further studies of the effect of nanotube fluctuations on cellular functions.

We explore the role of stochasticity and noise in the statistical outcomes of commonly studied population dynamics models within a space-independent (mean-field) perspective. Specifically, we consider a distributed population with logistic growth at each location, subject to “seascape” noise, wherein the population's fitness randomly varies with location and time. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently, and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.

Nanomechanical oscillators have, over the last few years, started probing regimes where quantum fluctuations are important. Here we consider a nonlinear parametric oscillator in the quantum domain. We show that in the classical subharmonic resonance zone, the quantum fluctuations are finite but greatly magnified depending on the strength of the nonlinear coupling. This should make such oscillators useful in probing quantum fluctuations.

Cell penetration by high aspect-ratio vertical nanostructures such as nanowires and nanopillars provides a powerful method for accessing the cell interior for delivery and sensing. However, there is a lack of studies on the understanding of the mechanism of cell membrane penetration and how design nanostructures to optimize the efficiency of penetration remains unclear. Here, we propose an analytical model to elucidate the mechanism of cells penetration by analyzing the free-energy change of cells adhered to the nanostructures surface. Furthermore, we provide a simple method to evaluate the crossover radius or density for cell membrane penetration. By introducing a dimensionless parameter, i.e., adhesion area factor, we investigated the effects of the radius and distribution densities of nanostructures on cell membrane penetration which is determined by the competition between adhesion energy and deformation energy. Besides, a diagram of the distribution of cell penetration and no penetration is obtained. From the cell penetration diagram, one can determine easily and intuitively the relations of cell penetration state with the radius and distribution densities of nanostructures. Our theoretical results seem to show broad agreement with experimental observations, which implies that these studies would provide useful guidance to the design of nanopatterned surfaces for biomedical applications.

Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology $3_1$, $4_1$, or $5_1$, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy $F$ with the end-to-end polymer extension length $X$ and examine the effect of varying the polymer topology, persistence length $P$, and cylinder diameter $D$ on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low $X$, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of $F$ with the position of a knot in conical channels for various values of the cone angle $\alpha$. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing $\alpha$ and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in $F$ is the change in the size of the hairpins as the knot moves to the wider region of the channel.

We analyze a molecular model to describe the phase transitions between the isotropic, nematic, smectic-A, and smectic-C phases. The smectic phases are described by the use of a pair potential, which lacks the full rotational symmetry because of the cylindrical symmetry around the smectic axis. The tilt of the long molecules inside the smectic layers is favored by a biquadratic pair potential, which compete with the pair potential of the McMillan model. The part of the phase diagram showing the first three phases is similar to that of the McMillan molecular model. The smectic-C phase is separated from the nematic by a continuous phase transition line along which the tilt angle is nonzero. The tilt angle vanishes continuously when one reaches the line separating the smectic-C and the smectic-A line.