In this paper, a generalization of the Cahn-Hilliard theory of binary liquids is presented for multicomponent incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion-type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free-energy functional is presented for an arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and we demonstrate that the energy penalization for multicomponent states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (four-component) systems. Simulations addressing liquid-flow-assisted spinodal decomposition in these systems are also presented.

This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of ${10}^{130}$) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential $\mu$ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase $\mu$ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed in this paper.

The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.

Efficiency at maximum power is found to be of the same order for a feedback ratchet and for its open-loop counterpart. However, feedback increases the output power up to a factor of five. This increase in output power is due to the increase in energy input and the effective entropy reduction obtained as a consequence of feedback. Optimal efficiency at maximum power is reached for time intervals between feedback actions two orders of magnitude smaller than the characteristic time of diffusion over a ratchet period length. The efficiency is computed consistently taking into account the correlation between the control actions. We consider a feedback control protocol for a discrete feedback flashing ratchet, which works against an external load. We maximize the power output optimizing the parameters of the ratchet, the controller, and the external load. The maximum power output is found to be upper bounded, so the attainable extracted power is limited. After, we compute an upper bound for the efficiency of this isothermal feedback ratchet at maximum power output. We make this computation applying recent developments of the thermodynamics of feedback-controlled systems, which give an equation to compute the entropy reduction due to information. However, this equation requires the computation of the probability of each of the possible sequences of the controller's actions. This computation becomes involved when the sequence of the controller's actions is non-Markovian, as is the case in most feedback ratchets. We here introduce an alternative procedure to set strong bounds to the entropy reduction in order to compute its value. In this procedure the bounds are evaluated in a quasi-Markovian limit, which emerge when there are big differences between the stationary probabilities of the system states. These big differences are an effect of the potential strength, which minimizes the departures from the Markovianicity of the sequence of control actions, allowing also to minimize the departures from the optimal performance of the system. This procedure can be applied to other feedback ratchets and, more in general, to other control systems.

We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.

A dissipative system with asymmetric interaction, the optimal velocity model, shows a Hopf bifurcation concerned with the transition from a homogeneous motion to the formation of a moving cluster, such as the emergence of a traffic jam. We investigate the properties of Hopf bifurcation depending on the particle density, using the dynamical system for the traveling cluster solution of the continuum system derived from the original discrete system of particles. The Hopf bifurcation is revealed as a subcritical one, and the property explains well the specific phenomena in highway traffic: the metastability of jamming transition and the hysteresis effect in the relation of car density and flow rate.

We investigate the impact of people's perceptions regarding the risk of an epidemic by analyzing the differences between local and global risk perceptions on affecting the epidemic threshold. Three issues are introduced to explain such differences: the indirect risk source, the heterogeneous global risk, and heterogeneity in individuals' intrinsic susceptibilities. When the direct risk source is completely undetected, the local risk perception tends to have no effect on the epidemic threshold, and the effect of the local risk is nearly equivalent to that of the global risk perception, thereby also suggesting a reason why global risk perception cannot affect the epidemic threshold. However, there is a surprising effect of the global risk perception: When its heterogeneity is sufficiently high, an increased epidemic threshold value sometimes may lead to a greater infected ratio.

Through numerically solving the appropriate wave equations, propagation of biosonar signals in a Chinese river dolphin (baiji) was studied. The interfacial waves along the rostrum-tissue interfaces, including both compressional (longitudinal) and shear (transverse) waves in the solid rostrum through fluid-solid coupling were examined. The baiji's rostrum was found to effect acoustic beam formation not only as an interfacial wave generator but also as a sound reflector. The wave propagation patterns in the solid rostrum were found to significantly change the wave movement through the bone. Vibrations in the rostrum, expressed in solid displacement, initially increased but eventually decreased from posterior to anterior sides, indicating a complex physical process. Furthermore, the comparisons among seven cases, including the combination of (1) the rostrum, melon, and air sacs; (2) rostrum–air sacs; (3) rostrum-melon; (4) only rostrum; (5) air sacs–melon; (6) only air sacs; and (7) only melon revealed that the cases including the rostrum were better able to approach the complete system by inducing rostrum-tissue interfacial waves and reducing the differences in main beam angle and −3 dB beam width. The interfacial waves in the rostrum were considered complementary with reflection to determine the obbligato role of the rostrum in the baiji's biosonar emission. The far-field beams formed from complete fluid-solid models and non-fluid-solid models were compared to reveal the effects brought by the consideration of shear waves of the solid structures of the baiji. The results may provide useful information for further understanding the role of the rostrum in this odontocete species.

By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension $d\to \infty$, and it can be improved systematically by adding more terms in the expansion.

We derive an analytical formula for the Saturn-ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we obtain an explicit expression for the ring radius and its dependence on the anchoring energy. We work within Landau–de Gennes theory: Nematic alignment is described by a tensorial order parameter. For nematic colloids this model had previously been used exclusively to perform numerical computations. Our method demonstrates that the tensorial theory can also be used to obtain analytical results, suggesting a different approach to the understanding of nematic colloidal interactions.

The ultimate semiclassical wave packet propagation technique is a complex, time-dependent Wentzel-Kramers-Brillouin method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out fully in practice. In its place roughly twenty years ago, linearized wave packet dynamics was generalized to methods that include sets of off-center, real trajectories for both classically integrable and chaotic dynamical systems that completely capture the dynamical transport. The connections between those methods and GGWPD are developed in a way that enables a far more practical implementation of GGWPD. The generally complex saddle-point trajectories at its foundation are found using a multidimensional Newton-Raphson root search method that begins with the set of off-center, real trajectories. This is possible because there is a one-to-one correspondence. The neighboring trajectories associated with each off-center, real trajectory form a path that crosses a unique saddle; there are exceptions that are straightforward to identify. The method is applied to the kicked rotor to demonstrate the accuracy improvement as a function of $\hslash$ that comes with using the saddle-point trajectories.

Von Willebrand factor (VWF) multimers are large adhesive proteins that are essential to the initiation of hemostatic plugs at sites of vascular injury. The binding of VWF multimers to platelets, as well as VWF proteolysis, is regulated by shear stresses that alter VWF multimeric conformation. We used single molecule manipulation with atomic force microscopy (AFM) to investigate the effect of high fluid shear stress on soluble dimeric and multimeric forms of VWF. VWF dimers are the smallest unit that polymerizes to construct large VWF multimers. The resistance to mechanical unfolding with or without exposure to shear stress was used to evaluate VWF conformational forms. Our data indicate that, unlike recombinant VWF multimers (RVWF), recombinant dimeric VWF (RDVWF) unfolding force is not altered by high shear stress $(100{\text{dynes/cm}}^2$ for 3 min at ${37}^{\circ }\mathrm{C})$. We conclude that under the shear conditions used $(100{\text{dynes/cm}}^2$ for 3 min at ${37}^{\circ }\mathrm{C}\mathrm{)}$, VWF dimers do not self-associate into a conformation analogous to that attained by sheared large VWF multimers.

Transport properties of a suspension of solid particles in a viscous gas are studied. The dissipation in such systems arises from two sources: inelasticity in particle collisions and viscous dissipation due to the effect of the gas phase on the particles. Here we consider a simplified case in which the mean relative velocity between the gas and solid phases is taken to be zero, such that “thermal drag” is the only remaining gas-solid interaction. Unlike the previous, more general, treatment of the drag force [Garzó et al., J. Fluid Mech. 712, 129 (2012)], here we take into account contributions to the (scaled) transport coefficients ${\eta }^{*}$ (shear viscosity), ${\kappa }^{*}$ (thermal conductivity), and ${\mu }^{*}$ (Dufour-like coefficient) coming from the temperature dependence of the (dimensionless) friction coefficient ${\gamma }^{*}$ characterizing the amplitude of the drag force. At moderate densities, the thermal drag model (which is based on the Enskog kinetic equation) is solved by means of the Chapman-Enskog method and the Navier-Stokes transport coefficients are determined in terms of the coefficient of restitution, the solid volume fraction, and the friction coefficient. The results indicate that the effect of the gas phase on ${\eta }^{*}$ and ${\mu }^{*}$ is non-negligible (especially in the case of relatively dilute systems) while the form of ${\kappa }^{*}$ is the same as the one obtained in the dry granular limit. Finally, as an application of these results, a linear stability analysis of the hydrodynamic equations is carried out to analyze the conditions for stability of the homogeneous cooling state. A comparison with direct numerical simulations shows a good agreement for conditions of practical interest.

The linear spatiotemporal response to an infinitesimal disturbance is analyzed for an electrified falling film based on the Orr-Sommerfeld boundary value problem. Four spatial branches are identified, which lose their spatial symmetry in the presence of an electric field. In addition, the absolute and convective instabilities are studied within the frameworks of the saddle point approach and the collision criterion. The collision criterion offers two unstable branches that characterize the exact range of the unstable wave packet that is diminished in the presence of an electric field. In contrast, the saddle point approach offers only one unstable branch. The associated unstable range of the wave packet is similar to that predicted by the collision criterion only when the electric field is enhanced. It is shown that the electrified falling film is convectively unstable.

The generation of high-intensity attopulses has been investigated in cylindrical geometry by using a three-dimensional particle-in-cell plasma simulation code. Due to the rotation-symmetric target, a circularly polarized laser pulse is considered, propagating on the axis of a hollow conelike target. The large incidence angle and constant ponderomotive pressure lead to nanobunching of relativistic electrons responsible for the laser-driven synchrotron emission. A numerical method is developed to find the source and direction of the coherent radiation that ensures the existence of attopulses. The intensity modulation in the harmonic spectrum is well described by the model of coherent synchrotron emission extended to the regime of higher order $\gamma$ spikes. The spatial distribution of the higher harmonics resembles a spiral shape which gets focused into a small volume behind the target.

The nonlinear optical response of a dilute atomic gas to ultrashort high-intensity midinfrared pulse excitation is calculated fully microscopically. The optically induced polarization dynamics is evaluated for the interacting many-electron system in a gas of hydrogen atoms. It is shown that the many-body effects during the excitation distinctly influence not only the atomic ionization dynamics, but also the nonlinear polarization response in the midinfrared regime. The delicate balance between the Kerr focusing and the ionization-induced defocusing is dramatically modified and a significant decrease of the nonlinear refractive index is predicted for increasing wavelength of the exciting pulse.

The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various pointlike defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a $\frac{1}{2}\langle 111\rangle \left\{110\right\}$ edge dislocation in BCC iron. We have implemented immobile spherical precipitates into the ParaDis discrete dislocation dynamics code, with the dislocations interacting with the precipitates via a Gaussian potential, generating a normal force acting on the dislocation segments. The parameters used in the discrete dislocation dynamics simulations for the precipitate potential, the dislocation mobility, shear modulus, and dislocation core energy are obtained from molecular dynamics simulations. We compare the critical stresses needed to unpin the dislocation from the precipitate in molecular dynamics and discrete dislocation dynamics simulations in order to fit the two methods together and discuss the variety of the relevant pinning and depinning mechanisms.