Stokes' hypothesis, the zeroing of the bulk viscosity in a Newtonian fluid, is discussed in this paper. To this aim, a continuum macroscopic fluid domain is initially modeled as a Hamiltonian system of discrete particles, for which the interparticle dissipative forces are required to be radial in order to conserve the angular momentum. The resulting system of particles is then reconverted to the continuum domain via the framework of the smoothed particle hydrodynamics (SPH) model. Since an SPH-consistent approximation of the Newtonian viscous term in the momentum equation incorporates interparticle radial as well as nonradial terms, it is postulated that the latter must be null. In the present work it is shown that this constraint implies that first and second viscosities are equal, resulting in a positive value for the bulk viscosity, in contradiction to the cited Stokes' hypothesis. Moreover, it is found that this postulate leads to bulk viscosity coefficients close to values found in the experimental literature for monoatomic gases and common liquids such as water.

We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbors on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbor couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wave vector.

Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949)] to capture the emergence of dissipative effects in relativistic fluids.

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

Trophallaxis, the regurgitation and mouth to mouth transfer of liquid food between members of eusocial insect societies, is an important process that allows the fast and efficient dissemination of food in the colony. Trophallactic systems are typically treated as a network of agent interactions. This approach, though valuable, does not easily lend itself to analytic predictions. In this work we consider a simple trophallactic system of randomly interacting agents with finite carrying capacity, and calculate analytically and via a series of simulations the global food intake rate for the whole colony as well as observables describing how uniformly the food is distributed within the nest. Our model and predictions provide a useful benchmark to assess to what level the observed food uptake rates and efficiency in food distribution is due to stochastic effects or specific trophallactic strategies by the ant colony. Our work also serves as a stepping stone to describing the collective properties of more complex trophallactic systems, such as those including division of labor between foragers and workers.

We study the slow stochastic dynamics near the depinning threshold of an elastic interface in a random medium by solving a particularly suited model of hopping interacting particles that belongs to the quenched-Edwards-Wilkinson depinning universality class. The model allows us to compare the cases of uniformly activated and Arrhenius activated hops. In the former case, the velocity accurately follows a standard scaling law of the force and noise intensity with the analog of the thermal rounding exponent satisfying a modified “hyperscaling” relation. For the Arrhenius activation, we find, both numerically and analytically, that the standard scaling form fails for any value of the thermal rounding exponent. We propose an alternative scaling incorporating logarithmic corrections that appropriately fits the numerical results. We argue that this anomalous scaling is related to the strong correlation between activated hops that, alternated with deterministic depinning-like avalanches, occur below the depinning threshold. We rationalize the spatiotemporal patterns by making an analogy of the present model in the near-threshold creep regime with some well-known models with extremal dynamics, particularly the Bak-Sneppen model.

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of $\mu$-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent $\beta$ and the roughness exponent $\alpha$. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of $\mu$-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent $\beta$ and to confirm the validity of our numerical analysis.

Geometric Brownian motion (GBM) is frequently used to model price dynamics of financial assets, and a weighted average of multiple GBMs is commonly used to model a financial portfolio. Diversified portfolios can lead to an increased exponential growth compared to a single asset by effectively reducing the effective noise. The sum of GBM processes is no longer a log-normal process and has a complex statistical properties. The nonergodicity of the weighted average process results in constant degradation of the exponential growth from the ensemble average toward the time average. One way to stay closer to the ensemble average is to maintain a balanced portfolio: keep the relative weights of the different assets constant over time. To keep these proportions constant, whenever assets values change, it is necessary to rebalance their relative weights, exposing this strategy to fees (transaction costs). Two strategies that were suggested in the past for cases that involve fees are rebalance the portfolio periodically and rebalance it in a partial way. In this paper, we study these two strategies in the presence of correlations and fees. We show that using periodic and partial rebalance strategies, it is possible to maintain a steady exponential growth while minimizing the losses due to fees. We also demonstrate how these redistribution strategies perform in a phenomenal way on real-world market data, despite the fact that not all assumptions of the model hold in these real-world systems. Our results have important implications for stochastic dynamics in general and to portfolio management in particular, as we show that there is a superior alternative to the common buy-and-hold strategy, even in the presence of correlations and fees.

Many spherical viruses encapsulate their genomes in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genomes. We model the effect of the nonuniform icosahedral charge distribution from the protein shell instead using a mean-field theory. We find that this nonuniform charge distribution strongly affects the optimal genome length and that it can explain the experimentally observed phenomenon of overcharging of virus and viruslike particles.

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability $\eta \left(r_c\right)$ that the distance between the chain extremities is smaller than some capture radius $r_c$. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

The salt-induced microheterogeneity (MH) formation in binary liquid mixtures is studied by small-angle x-ray scattering (SAXS) and liquid state theory. Previous experiments have shown that this phenomenon occurs for antagonistic salts, whose cations and anions prefer different components of the solvent mixture. However, so far the precise mechanism leading to the characteristic length scale of MHs has remained unclear. Here, it is shown that MHs can be generated by the competition of short-ranged interactions and long-ranged monopole-dipole interactions. The experimental SAXS patterns can be reproduced quantitatively by fitting to the derived correlation functions without assuming any specific model. The dependency of the MH structure with respect to ionic strength and temperature is analyzed. Close to the demixing phase transition, critical-like behavior occurs with respect to the spinodal line in the phase diagram.

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a “weak” temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, $1/D{\kappa }^2$, where $D$ is the Brownian diffusion coefficient of both ion species, and ${\kappa }^{-1}$ is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, $L^2/D$, where $L$ is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

The paper deals with a theoretical study of the effective shear modulus of a magnetic gel, consisting of magnetizable particles randomly and isotropically distributed in an elastic matrix. The effect of an external magnetic field on the composite modulus is the focus of our consideration. We take into account that magnetic interaction between the particles can induce their spatial rearrangement and lead to internal anisotropy of the system. Our results show that, if this magnetically induced anisotropy is insignificant, the applied field reduces the total shear modulus of the composite. Strong anisotropy can qualitatively change the magnetomechanic effect and induce an increase of this modulus with the field.

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature—it vanishes on a nonzero measure set in orientation space.

A negative extensibility material structure pulls back and contracts when the external tensile load reaches a certain critical level. In this paper, we reveal basic mathematical features of the nonlinear strain energy function responsible for this unusual mechanical property. A systematic discussion leads to a comprehensive phase diagram in terms of design parameters for a simple unit cell structure that provides a panoramic view of all possible nonlinear mechanical behaviors. A negative extensibility region clearly is identified in the diagram. The sought property is seen to be rare, occurring only for a very narrow range of the design parameters. Nonetheless, due to the simplicity of the studied structure we suggest that the negative extensibility should be a more common phenomenon than previously thought. It can appear in simple bistable cells made of only several linearly elastic links, although at some peculiar combinations of their properties. These bistable unit cells can be used to design periodic mechanical metamaterials whose examples are shown as well as innovative architectural metastructures.

We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there were contrasting effects of slurry thickness on the probability distribution of the polygonal cell area. The experimental findings are believed to result from the difference in the shape and size of starch grains, which strongly influence the capillary transport of water and tensile stress field that drives the polygonal cracking.

The description of the Moffatt and Parker problem recently revisited by O. Pezzi et al. [Astrophys. J. 834, 166 (2017)] is here extended by analyzing the features of the turbulence produced by the interaction of two colliding Alfvénic wave packets in a kinetic plasma. Although the approach based on the presence of linear modes features is still helpful in characterizing some low-energy fluctuations, other signatures, which go beyond the pure linear modes analysis, are recovered, such as the significant weakening of clear dispersion relations and the production of zero frequency fluctuations.

We consider capillary condensation transitions occurring in open slits of width $L$ and finite height $H$ immersed in a reservoir of vapor. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit ($H=\infty$) due to the presence of two menisci that are pinned near the open ends. Using macroscopic arguments, we derive a modified Kelvin equation for the pressure $p_{cc}(L;H)$ at which condensation occurs and show that the two menisci are characterized by an edge contact angle ${\theta }_e$ that is always larger than the equilibrium contact angle $\theta$, only equal to it in the limit of macroscopic $H$. For walls that are completely wet ($\theta =0$) the edge contact angle depends only on the aspect ratio of the capillary and is well described by ${\theta }_e\approx \sqrt{\pi L/2H}$ for large $H$. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature $T_w$ we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above $T_w$ the modified Kelvin equation only becomes accurate for much larger systems.

A cyclically working quantum-mechanical engine that operates at a single temperature is proposed. Its energy input is delivered by a quantum measurement. The functioning of the engine does not require any feedback control. We analyze work, heat, and the efficiency of the engine for the case of a working substance that is governed by the laws of quantum mechanics and that can be adiabatically compressed and expanded. The obtained general expressions are exemplified for a spin in an adiabatically changing magnetic field and a particle moving in a potential with slowly changing shape.

In a description of physical systems with Langevin equations, interacting degrees of freedom are usually coupled through symmetric parameter matrices. This coupling symmetry is a consequence of time-reversal symmetry of the involved conservative forces. If coupling parameters fluctuate randomly, the resulting noise is called multiplicative. For example, mechanical oscillators can be coupled through a fluctuating, symmetric matrix of spring “constants.” Such systems exhibit well-studied instabilities. In this article, we study the complementary case of antisymmetric, time-reversal symmetry-breaking coupling that can be realized with Lorentz forces or various gyrators. We consider the case in which these antisymmetric couplings fluctuate. This type of multiplicative noise does not lead to instabilities in the stationary state but renormalizes the effective nonequilibrium friction. Fluctuating Lorentz-force-like couplings also allow one to control and rectify heat transfer. A noteworthy property of this mechanism of producing asymmetric heat flux is that the controlling couplings do not exchange energy with the system.