Molar fractions are used in applied diffusion kinetics for incorporating thermodynamic and kinetic databases. Molar quantities (molar concentration and molar flux) and reduced molar quantities (molar fraction and reduced molar flux) usually are regarded to be equivalent; i.e., molar quantities are replaced with their reduced forms. However, as the fluxes are related to material properties, the diffusion equations expressed in molar fractions are not consistent with the normalization condition of molar fractions. We develop diffusion kinetics consistent with this condition. Our method is applicable to diffusion with total reduced flux, such as diffusion in an external field or flow field. As two case studies, the developed method is used to investigate ionic diffusion in an electrolyte solution and ionic demixing in a semiconductor oxide.

Single-particle tracking (SPT) is a versatile tool for quantifying diffusional motion in complex soft-matter systems, e.g., in biological specimen. Evaluating SPT data often invokes the fitting of a trajectory's time-averaged mean-square displacement (TA-MSD) with a simple power law, ${\langle r^2\left(\tau \right)\rangle }_t\sim {\tau }^{\alpha }$, where the scaling exponent $\alpha$ can yield important insights into the nature of the transport process. Biological specimen, for example, frequently feature a diffusion anomaly, i.e., an exponent $\alpha <1$ (“subdiffusion”). However, due to SPT-inherent static and dynamic localization errors, in combination with typically short trajectories, it is often a real challenge to determine the value of $\alpha$ reliably by simply fitting TA-MSDs. Here a straightforward resampling approach is presented and tested that eliminates both localization errors in the TA-MSD of trajectories originating from subdiffusive fractional Brownian motion processes. As a result, the mean anomaly exponent ${\langle \alpha \rangle }_E$ of an ensemble of trajectories is revealed in a robust fashion.

Despite considerable progress during the past decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg time $T_H$) is still missing. This challenge, corresponding to resolving spectral structures on energy scales below the mean level spacing, is intimately related to the quest for semiclassically restoring unitary quantum evolution. Guided through insights for quantum graphs we devise a periodic-orbit resummation procedure for spectra of quantum chaotic systems invoking periodic-orbit self-encounters as the structuring element of a hierarchical phase space dynamics. Quantum unitarity is reflected in real-valued spectral determinants with zeros giving discrete energy levels. We propose a way to purely semiclassically construct such real spectral determinants based on two major underlying mechanisms. (i) Complementary contributions to the spectral determinant from regrouped pseudo-orbits of duration $T<T_H$ and $T_H-T$ are complex conjugate to each other. (ii) Contributions from long periodic orbits involving multiple traversals along shorter orbits cancel out. We furthermore discuss implications for interacting $N$-particle quantum systems with a chaotic classical large-$N$ limit that have recently attracted particular interest in the context of many-body quantum chaos.

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force, as previous work has often done, is thermodynamically inconsistent and can overestimate the stall force, sometimes by more than a factor of two. We perform simulations and analytic calculations of the force-velocity relation satisfying the thermodynamic relationship. The force-velocity relation can deviate strongly from the Brownian-Ratchet predictions. For shallow potential wells of depth $\sim 5k_{B}T$, which might correspond to transient filament-membrane attachments, the velocity drops more rapidly than predicted by the Brownian-Ratchet model, in some cases by as much as a factor of 50 at an opposing force of only 1 pN. On the other hand, the zero-force velocity is much less affected than would be expected from naive use of the Boltzmann factor. Furthermore, the growth velocity has a surprisingly strong dependence on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing but only if the attractive well is relatively flat over a region comparable to or greater than the monomer size. For double-well potentials, which have such a flat region, the slowing of polymerization by external pushing force is almost linear up to the stall force in some parameter ranges.

The anomalous Ostrovsky equation, which describes waves in vertically sheared ocean flows and magnetoacoustic waves, possesses steadily propagating, finite-amplitude, localized wave-packet solutions. It is shown here that these solutions can be obtained asymptotically, using Whitham modulation theory, as the solution to a nonlinear eigenvalue problem. This allows the various wave-packet solutions to be delineated and compared to solutions of the full equations of motion. A periodic solution with an embedded wave train is also constructed.

We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the “flight-crash” events reported by Xu et al. [Proc. Natl. Acad. Sci. (USA) 111, 7558 (2014)]. We perform systematic studies to trace the origins of this suppression in the emergent geometry of the flow and show why such a Lagrangian measure of irreversibility may fail in the presence of rotation.

Warm dense carbon is generated at 0.3–2.0 g/cc and 1–7 eV by proton heating. The release equation of state (EOS) after heating and thermal conductivity of warm dense carbon are studied experimentally in this regime using a Au/C dual-layer target to initiate a temperature gradient and two picosecond time-resolved diagnostics to probe the surface expansion and heat flow. Comparison between the data and simulations using various EOSs and thermal conductivity models is quantified with a statistical ${\chi }^2$ analysis. Out of seven EOS tables and five thermal conductivity models, only L9061 with the Lee-More model provides a probability above 50% to match all data.

By combining two generalized-ensemble algorithms, the replica-exchange Wang-Landau (REWL) method and the multicanonical replica-exchange method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model using the three methods, namely REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by REWL-MUCAREM is more accurate than that is estimated by the two methods separately.

The present paper reports on an investigation of the effect of the interface layers in enhancing thermal conductivity of Cu-Ar nanofluids. The approach is based on linear response theory combined with equilibrium molecular dynamics simulations. For a wettability parameter of 1.4 and volume fraction of $5.8\%$, simulation results show enhancements in thermal conductivity as high as $50\%$. Among others, the most salient result concerns the contribution of the vibration modes of liquid Ar atoms around Cu nanoparticles (NPs) in enhancing thermal conductivity of the nanofluid. Our findings reveal that these vibration modes coincide on a large domain of frequencies ($10-50{\mathrm{ps}}^{-1}$) with those of Cu atoms of the NPs. The enhancement of the thermal conductivity was explained by the increase of vibrational mean-free paths.

Simulations with more than ${10}^{12}$ spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field $H$. The interface advances in a series of avalanches whose size diverges at a critical external field $H_c$. Finite-size scaling is applied to determine critical exponents and test scaling relations. Growth is intrinsically anisotropic with the height of an avalanche normal to the interface ${\ell }_{\perp }$ scaling as the width along the interface ${\ell }_{\parallel }$ to a power $\chi =0.85\pm 0.01$. The total interface roughness is consistent with self-affine scaling with a roughness exponent $\zeta \approx \chi$ that is much larger than values found previously for the RFIM and related models that explicitly break orientational symmetry by requiring the interface to be single-valued. Because the RFIM maintains orientational symmetry, the interface develops overhangs that may surround unfavorable regions to create uninvaded bubbles. Overhangs complicate measures of the roughness exponent but decrease in importance with increasing system size.

We consider networks formed from two populations of identical oscillators, with uniform strength all-to-all coupling within populations and also between populations with a different strength. Such systems are known to support chimera states in which oscillators within one population are perfectly synchronized while in the other the oscillators are incoherent and have a different mean frequency from those in the synchronous population. Assuming that the oscillators in the incoherent population always lie on a closed smooth curve $\mathcal{C}$, we derive and analyze the dynamics of the shape of $\mathcal{C}$ and the probability density on $\mathcal{C}$ for four different types of oscillators. We put some previously derived results on a more rigorous footing and analyze two new systems.

Using the combination of the kinetic theory of gases (KTG), Boltzmann transport equation (BTE), and molecular dynamics (MD) simulations, we study the transport phenomena in the Knudsen layer near a planar evaporating surface. The MD simulation is first used to validate the assumption regarding the anisotropic velocity distribution of vapor molecules in the Knudsen layer. Based on this assumption, we use the KTG to formulate the temperature and density of vapor at the evaporating surface as a function of the evaporation rate and the mass accommodation coefficient (MAC), and we use these vapor properties as the boundary conditions to find the solution to the BTE for the anisotropic vapor flow in the Knudsen layer. From the study of the evaporation into a vacuum, we show the ratio of the macroscopic speed of vapor to the most probable thermal speed of vapor molecules in the flow direction will always reach the maximum value of $\sqrt{1.5}$ at the vacuum boundary. The BTE solutions predict that the maximum evaporation flux from a liquid surface at a given temperature depends on both the MAC and the distance between the evaporating surface and the vacuum boundary. From the study of the evaporation and condensation between two parallel plates, we show the BTE solutions give good predictions of transport phenomena in both the anisotropic vapor flow within the Knudsen layer and the isotropic flow out of the Knudsen layer. All the predictions from the BTE are verified by the MD simulation results.

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial, and biological networks. At odds with empirical observations, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a theoretical explanation for the observation of large-scale contagion in highly connected but heterogeneous networks.

Recent studies report on anomalous spin transport for the integrable Heisenberg spin chain at its isotropic point. Anomalous scaling is also observed in the time evolution of nonequilibrium initial conditions, the decay of current-current correlations, and nonequilibrium steady state averages. These studies indicate a space-time scaling with $x\sim t^{2/3}$ behavior at the isotropic point, in sharp contrast to the ballistic form $x\sim t$ generically expected for integrable systems. In our contribution we study the scaling behavior for the integrable lattice Landau-Lifshitz spin chain. We report on equilibrium spatiotemporal correlations and dynamics with step initial conditions. Remarkably, for the case with zero mean magnetization, we find strong evidence that the scaling function is identical to the one obtained from the stationary stochastic Burgers equation, alias Kardar-Parisi-Zhang equation. In addition, we present results for the easy-plane and easy-axis regimes for which, respectively, ballistic and diffusive spin transport is observed, whereas the energy remains ballistic over the entire parameter regime.

The recently developed formalism of nonlinear fluctuating hydrodynamics (NLFH) has been instrumental in unraveling many new dynamical universality classes in coupled driven systems with multiple conserved quantities. In principle, this formalism requires knowledge of the exact expression of locally conserved current in terms of local density of the conserved components. However, for most nonequilibrium systems an exact expression is not available and it is important to know what happens to the predictions of NLFH in these cases. We address this question here in a system with coupled time evolution of sliding particles on a fluctuating energy landscape. In the disordered phase this system shows short-ranged correlations, the exact form of which is not known, and so the exact expression for current cannot be obtained. We use approximate expressions based on mean-field theory and corrections to it, to test the prediction of NLFH using numerical simulations. In this process we also discover important finite size effects and show how they affect the predictions of NLFH. We find that our system is rich enough to show a large variety of universality classes. From our analytics and simulations we have been able to find parameter values which lead to diffusive, Karder-Parisi-Zhang (KPZ), $5/3$ Lévy, and modified KPZ universality classes. Interestingly, the scaling function in the modified KPZ case turns out to be close to the Prähofer-Spohn function, which is known to describe usual KPZ scaling. Our analytics also predict the golden mean and the $3/2$ Lévy universality classes within our model but our simulations could not verify this, perhaps due to strong finite size effects.

We analyze a generalization of the hard-sphere dipole system in two dimensions in which the range of the interaction can be varied. We focus on the system in the limit in which the interaction becomes increasingly short ranged, while the temperature becomes low. By using a cluster expansion and taking advantage of low temperatures to perform saddle-point approximations, we argue that a well-defined double limit exists in which the only structures which contribute to the free energy are chains. We then argue that the dominance of chain structures is equivalent to the dominance of chain diagrams in a cluster expansion, but only if the expansion is performed around a hard-sphere system (rather than the standard ideal gas). We show that this leads to nonstandard factorization rules for diagrams and use this to construct a closed-form expression for the free energy at low densities. We then compare this construction to several models previously developed for the hard-sphere dipole system in the regime where chain structures dominate and argue that the comparison provides evidence in favor of one model over the others. We also use this construction to incorporate some finite-density effects though the hard-sphere radial distribution function and analyze how these effects impact chain length and the equation of state.

We study the effect of superradiance in open quantum systems, i.e., the separation of short- and long-living eigenstates when a certain subspace of states in the Hilbert space acquires an increasing decay width. We use several Hamiltonian forms of the initial closed system and generate their coupling to continuum by means of the random matrix theory. We average the results over a large number of statistical realizations of an effective non-Hermitian Hamiltonian and relate robust features of the superradiance process to the distribution of its exceptional points. We show that the superradiance effect is enhanced if the initial system is at the point of quantum criticality.

Many complex systems are characterized by time-varying patterns of interactions. These interactions comprise strong ties, driven by dyadic relationships, and weak ties, based on node-specific attributes. The interplay between strong and weak ties plays an important role on dynamical processes that could unfold on complex systems. However, seldom do we have access to precise information about the time-varying topology of interaction patterns. A particularly elusive question is to distinguish strong from weak ties, on the basis of the sole node dynamics. Building upon analytical results, we propose a statistically-principled algorithm to reconstruct the backbone of strong ties from data of a spreading process, consisting of the time series of individuals' states. Our method is numerically validated over a range of synthetic datasets, encapsulating salient features of real-world systems. Motivated by compelling evidence, we propose the integration of our algorithm in a targeted immunization strategy that prioritizes influential nodes in the inferred backbone. Through Monte Carlo simulations on synthetic networks and a real-world case study, we demonstrate the viability of our approach.

Nuclear magnetic resonance (NMR) diffusion pore imaging has been proposed to study the shape of arbitrary closed pores filled with an NMR-detectable medium by use of nonclassical diffusion encoding schemes. Potential applications can be found in biomedical imaging and porous media research. When studying non-point-symmetric pores, NMR signals with nonvanishing imaginary parts arise containing the pore shape information, which is lost for classical diffusion encoding schemes. Key limitations are the required high magnetic field gradient amplitudes and $T$2 relaxation while approaching the diffusion long-time limit. To benefit from the slower $T$1 decay, we demonstrate the feasibility of diffusion pore imaging with stimulated echoes using Monte Carlo simulations and experiments with hyperpolarized xenon-129 gas in well-defined geometries and show that the necessary complex-valued signals can be acquired. Analytical derivation of the stimulated echo double diffusion encoded signal was performed to investigate the effect of the additionally arising undesired terms on the complex phase information. These terms correspond to signals arising for spin-echo sequences with unbalanced gradients. For most possible applications, the unbalanced terms can be neglected. If non-negligible, selection of the appropriate signal component using a phase cycling scheme was demonstrated experimentally. Using stimulated echoes may be a step towards application of diffusion pore imaging to larger pores with gradient amplitudes available today in preclinical systems.

The effect of line tension on the axisymmetric nanoscale capillary bridge between two identical substrates with convex, concave, and flat geometry at the liquid-vapor equilibrium is theoretically studied. The modified Young's equation for the contact angle, which takes into account the effect of line tension, is derived on a general axisymmetric curved surface using the variational method. Even without the effect of line tension, the parameter space where the bridge can exist is limited simply by the geometry of substrates. The modified Young's equation further restricts the space where the bridge can exist when the line tension is positive because the equilibrium contact angle always remains finite and the wetting state near the zero contact angle cannot be realized. It is shown that the interplay of the geometry and the positive line tension restricts the formation of capillary bridge.