We perform a tracer counterpermeation (TCP) analysis for a stochastic model of diffusive transport through a narrow linear pore where passing of species within the pore is inhibited or even excluded (single-file diffusion). TCP involves differently labeled but otherwise identical particles from two decoupled infinite reservoirs adsorbing into opposite ends of the pore, and desorbing from either end. In addition to transient behavior, we assess steady-state concentration profiles, spatial correlations, particle number fluctuations, and diffusion fluxes through the pore. From the profiles and fluxes, we determine a generalized tracer diffusion coefficient $D_{\mathrm{tr}}\left(x\right)$, at various positions $x$ within the pore. $D_{\mathrm{tr}}\left(x\right)$ has a plateau value in the pore center scaling inversely with the pore length, but it is enhanced near the pore openings. The latter feature reflects the effect of fluctuations in adsorption and desorption, and it is also associated with a nontrivial scaling of the concentration profiles near the pore openings.

The barrier energies for isomerization and fragmentation were measured for a series of retinal chromophore derivatives using a tandem ion mobility spectrometry approach. These measurements allow us to quantify the effect of charge delocalization on the rigidity of chromophores. We find that the role of the methyl group on the $C13$ position is pivotal regarding the ground state dynamics of the chromophore. Additionally, a correlation between quasi-equilibrium isomer distribution and fragmentation pathways is observed.

In this work we analyze the translocation of homopolymer chains poly-$X$, where $X$ represents any of the 20 naturally occurring amino acid residues, in terms of size $N$ and single-helical propensity $\omega$. We provide an analytical framework to calculate both the free energy $\mathcal{F}$ of translocation and the translocation time $\tau$ as a function of chain size $N$, energies $U$ and $\epsilon$ of the unfolded and folded states, respectively. Our results show that free energy $\mathcal{F}$ has a characteristic bell-shaped barrier as function of the percentage of monomers translocated. Inclusion of single-helical propensity $\omega$ associated to monomer $X$ and chain's native energy $\epsilon$ in the translocation model increases the energy barrier $\mathrm{\Delta }\mathcal{F}$ up to one order of magnitude as compared with the well-known Gaussian chain model. Computation of the mean first-passage time as function of chain size $N$ shows that the translocation time $\tau$ exhibits a significant jump of several orders of magnitude at a critical chain size $\mathcal{N}$. This jump markedly slows down translocation of chains larger than $\mathcal{N}$. Existence of the transition jump of $\tau$ has been observed experimentally at least in poly(ethylene oxide) chains [R. P. Choudhury, P. Galvosas, and M. Schönhoff, J. Phys. Chem. B 112, 13245 (2008)]. Our results suggest the transition jump of $\tau$ as a function of $N$ may be a very well spread feature throughout translocation of poly-$X$ chains.

Nonequilibrium coarse-grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield nonmonotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, $\mathrm{\Gamma }$, while the viscosity shows a monotonically increasing dependence on $\mathrm{\Gamma }$. This effect is shown to be independent of the degree of polymerization, $N$, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom-to-brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent ($\nu =0.5$, for θsolvent), but it is independent of the polymerization degree ($N$). On the other hand, the friction coefficient at the MBT scales as $\mu \sim N^{6/5}$, while the grafting density at the MBT scales as $\mathrm{\Gamma }\sim N^{-6/5}$ when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.

We investigate microgels synthesized from $N$-isopropylacrylamide (NIPAM) copolymerized with a large mol% of acrylic acid, finding that when the acid groups are partially ionized at high temperatures, competition between ion-induced swelling and hydrophobic deswelling of poly(NIPAM) chains results in microphase separation. In cross-linked microgels, this manifests as a dramatic decrease in the ratio between the radius of gyration and the hydrodynamic radius to $\sim 0.2$, indicating that almost all the mass of the microgel is concentrated near the particle center. We also observe a concurrent decrease of the polymer network length scale via small-angle neutron scattering, confirming the presence of a dense, deswollen core surrounded by a diffuse, charged periphery. We compare these results to those obtained for a system of charged ultralow-cross-linked microgels; the form factor shows a distinct peak at high $q$ when the temperature exceeds a threshold value. We successfully fit the form factor to theory developed to describe scattering from weakly charged gels in poor solvents, and we tie this behavior to charge segregation in the case of the cross-linked microgels.

High-resolution birefringence ($\mathrm{\Delta }n$) measurements are carried out to probe the critical behavior at the smectic-$A$–smectic-$C$ (Sm-$A$–Sm-$C$) phase transition in a binary system. The critical behavior of this transition is explored with the aid of a differential quotient extracted from the $\mathrm{\Delta }n$ values. The results obtained reveal that the Sm-$A$–Sm-$C$ and nematic–smectic-$A$ ($N$–Sm-$A$) transitions exhibit nonuniversal behaviors with effective exponents lying between the tricritical and three-dimensional $XY$ values and follow two distinctly different curves with decreasing width of the Sm-$A$ and $N$ phases, respectively. The origin of such critical behavior is a unique feature for the respective phase transitions.

A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components, thus leading to the emergence of strong and long-lived temperature anisotropies when the plasma is locally perturbed. An extended heat equation is shown to describe this process accurately.

Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle reservoir in terms of the pressure and the temperature of the reservoir. It is shown that equilibrium ideal gases and hard-disk systems with these boundary conditions reproduce statistical-mechanical properties based on the corresponding grand canonical distributions. We also apply the stochastic boundary conditions to a hard-disk model with a steady particle current escaping from a particle reservoir in an open tube, and discuss its nonequilibrium properties such as a chemical potential dependence of the current and deviations from the local equilibrium hypothesis.

We study the critical behavior and the ground-state entanglement of a large class of $\mathrm{su}\left(1\right|1)$ supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a $(1+1)$-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Rényi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of $(1+1)$-dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Our results confirm the widely believed conjecture that the critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.

Two important problems regarding spreading phenomena in complex topologies are the optimal selection of node sets either to minimize or maximize the extent of outbreaks. Both problems are nontrivial when a small fraction of the nodes in the network can be used to achieve the desired goal. The minimization problem is equivalent to a structural optimization. The “superblockers,” i.e., the nodes that should be removed from the network to minimize the size of outbreaks, are those nodes that make connected components as small as possible. “Superspreaders” are instead the nodes such that, if chosen as initiators, they maximize the average size of outbreaks. The identity of superspreaders is expected to depend not just on the topology, but also on the specific dynamics considered. Recently, it has been conjectured that the two optimization problems might be equivalent, in the sense that superblockers act also as superspreaders. In spite of its potential groundbreaking importance, no empirical study has been performed to validate this conjecture. In this paper, we perform an extensive analysis over a large set of real-world networks to test the similarity between sets of superblockers and of superspreaders. We show that the two optimization problems are not equivalent: superblockers do not act as optimal spreaders.

Being a rubber-like liquid crystalline elastomer, a nematic elastomer (NE) is anisotropic viscoelastic, and displays dynamic soft elasticity. In this paper, the transverse vibration of a NE Timoshenko beam is studied based on the linear viscoelasticity theory of nematic elastomers. The governing equation of motion for the transverse vibration of a NE Timoshenko beam is derived. A complex modal analysis method is used to obtain the natural frequencies and decrement coefficients of NE beams. The influences of the nematic director rotation, the rubber relaxation time, and the director rotation time on the vibration characteristic of NE Timoshenko beams are discussed in detail. The sensitivity of the dynamic performance of NE beams to director initial angle and relaxation times provides a possibility of intelligent controlling of their dynamic performance.

We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Furthermore we investigate how changes of the local deposition and erosion properties affect the final state of the porous structure, finding that the larger the range of wall shear stress for which there is neither erosion nor deposition, the more steady channels are formed in the structure.

Multistable systems exhibit a rich front dynamics between equilibria. In one-dimensional scalar gradient systems, the spread of the fronts is proportional to the energy difference between equilibria. Fronts spreading proportionally to the energetic difference between equilibria is a characteristic of one-dimensional scalar gradient systems. Based on a simple nonvariational bistable model, we show analytically and numerically that the direction and speed of front propagation is led by nonvariational dynamics. We provide experimental evidence of nonvariational front propagation between different molecular orientations in a quasi-one-dimensional liquid-crystal light valve subjected to optical feedback. Free diffraction length allows us to control the variational or nonvariational nature of this system. Numerical simulations of the phenomenological model have quite good agreement with experimental observations.

This work investigates the influence of geometrical features of the Apollonian packing (AP) on the behavior of magnetic models. The proposed model differs from previous investigations on the Apollonian network (AN), where the magnetic coupling constants depend only on the properties of the network structure defined by the packing, but not on quantitative aspects of its geometry. In opposition to the exact scale invariance observed in the AN, the circle's sizes in the AP are scaled by different factors when one goes from one generation to the next, requiring a different approach for the evaluation of the model's properties. If the nearest-neighbors coupling constants are defined by $J_{i,j}\sim 1/{(r_i+r_j)}^{\alpha }$, where $r_i$ indicates the radius of the circle $i$ containing the node $i$, the results for the correlation length $\xi$ indicate that the model's behavior depend on $\alpha$. In the thermodynamic limit, the uniform model ($\alpha =0$) is characterized by $\xi \to \infty$ for all $T>0$. Our results indicate that, on increasing $\alpha$, the system changes to an uncorrelated pattern, with finite $\xi$ at all $T>0$, at a value ${\alpha }_c\simeq 0.743$. For any fixed value of $\alpha$, no finite temperature singularity in the specific heat is observed, indicating that changes in the magnetic ordering occur only when $\alpha$ is changed. This is corroborated by the results for the magnetization and magnetic susceptibility.

We analyze the stochastic dynamics of a large population of noninteracting particles driven by a global environmental input in the form of a dichotomous Markov noise process (DMNP). The population density of particle states evolves according to a stochastic Liouville equation with respect to different realizations of the DMNP. We then exploit the connection with previous work on diffusion in randomly switching environments, in order to derive moment equations for the distribution of solutions to the stochastic Liouville equation. We illustrate the theory by considering two simple examples of dichotomous flows, a velocity jump process and a two-state gene regulatory network. In both cases we show how the global environmental input induces statistical correlations between different realizations of the population density.

Negative absolute temperatures were introduced into experimental physics by Purcell and Pound, who successfully applied this concept to nuclear spins; nevertheless, the concept has proved controversial: a recent article aroused considerable interest by its claim, based on a classical entropy formula (the “volume entropy”) due to Gibbs, that negative temperatures violated basic principles of statistical thermodynamics. Here we give a thermodynamic analysis that confirms the negative-temperature interpretation of the Purcell-Pound experiments. We also examine the principal arguments that have been advanced against the negative temperature concept; we find that these arguments are not logically compelling, and moreover that the underlying “volume” entropy formula leads to predictions inconsistent with existing experimental results on nuclear spins. We conclude that, despite the counterarguments, negative absolute temperatures make good theoretical sense and did occur in the experiments designed to produce them.

We study the radiative heat transfer between two semi-infinite half-spaces, bounded by conductive surfaces in contact with vacuum. This setup is interpreted as a four-terminal mesoscopic transport problem. The slabs and interfaces are viewed as bosonic reservoirs, coupled perfectly to a scattering center consisting of the two planes and vacuum. Using Rytov's fluctuational electrodynamics and assuming Kirchhoff's circuital law, we calculate the heat flow in each bath. This allows for explicit evaluation of a conductance matrix, from which one readily verifies Büttiker symmetry. Thus, radiative heat transfer in layered media with conductive interfaces becomes a Landauer-Büttiker transport problem.

We consider the optical fiber channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. Using the Feynman path-integral approach for the model, we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity is positive for large signal power. Therefore, this correction increases the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region.

Noise-induced escape from the domain of attraction of a nonhyperbolic chaotic attractor in a periodically excited nonlinear oscillator is further investigated. Deviations are found to be amplified at the primary homoclinic tangency from which the optimal force begins to fluctuate dramatically. Escaping trajectories turn out to possess several modes to pass through the saddle cycle on the basin boundary, and each mode corresponds to a certain type of value of the action plot, respectively. A subset of the pattern of fluctuational paths from the chaotic attractor is obtained, showing the existence of complicated singularities.