The Brownian motion and aggregation of particles in nanofluids often lead to the formation of solid-film-solid structures. The molecular thin film confined between nanoparticles may have non-negligible effects on thermal conduction among nanoparticles. Using nonequilibrium molecular dynamics simulations, we study thermal conduction across the Ag particle-Ar thin-film interface. If the film contains only one molecular layer, we find that the solid-film interfacial thermal resistance $R_{\mathrm{SF}}$ is about 1 order of magnitude smaller than the solid-liquid (bulk) interfacial thermal resistance $R_{\mathrm{SL}}$. If there are two or more molecular layers in the film, it is shown that $R_{\mathrm{SF}}$ increases rapidly toward $R_{\mathrm{SL}}$ as film thickness increases. By comparing the vibrational density of states of Ag atoms and Ar molecules in the film, we demonstrate that the low thermal resistance in the monolayer film case is caused by the resonant thermal transport between Ag particles and Ar thin films.

A recent study shows that the dipole elongation in the extended dipole model plays a significant role in the phase transitions of liquid crystal phases. In this paper, molecular dynamics (MD) simulations were performed for the dipole model with different distances between the two charges keeping the total dipole moment the same. The potential energy consists of the Lennard-Jones potential and the site-site electrostatic contribution of partial charges. Detailed analyses were made with respect to the average order parameters $\langle P_1\rangle$ and $\langle P_2\rangle$ as functions of density along with other thermodynamic properties. When the reduced dipole elongations are 0.16 and 0.32, respectively, it is shown that the chainlike structures in the low density regime, liquid phases with columnar and smectic orders, and solid phases are formed; the phase with nematic order is not present anymore. At 0.64, the phases with antiferroelectric order were favored. The transition is found at the reduced elongation 0.55. It shows that the phase transitions are quite sensitive to the molecular charge distribution; this simple system could exhibit rather rich phase behaviors, which represents a significant advance in identifying molecular and state parameters of the future ferroelectric liquids.

The Parker model for coronal heating is investigated through a high resolution simulation. An inertial range is resolved where fluctuating magnetic energy $E_{{}_M}(k_{\perp })\propto k_{\perp }^{-2.7}$ exceeds kinetic energy $E_{{}_K}(k_{\perp })\propto k_{\perp }^{-0.6}$. Increments scale as $\delta b_{{}_{\ell }}\simeq {\ell }^{-0.85}\text{and}\hspace{0.5em}\delta u_{{}_{\ell }}\simeq {\ell }^{+0.2}$ with velocity increasing at small scales, indicating that magnetic reconnection plays a prime role in this turbulent system. We show that spectral energy transport is akin to standard magnetohydrodynamic (MHD) turbulence even for a system of reconnecting current sheets sustained by the boundary. In this new MHD turbulent cascade, kinetic energy flows are negligible while cross-field flows are enhanced, and through a series of “reflections” between the two fields, cascade more than half of the total spectral energy flow.

The parameter-dependent spectral statistics of totally connected quantum graphs with $n=4-30$ vertices, such as the parametric velocities correlation functions and the distribution of curvatures, are studied. The inverse participation ratio (IPR), an important measure of localization effects, was also numerically investigated. In the calculations, we successfully used two different theoretical approaches. The first approach was based on the graphs’ eigenenergies and wave functions calculations, while the second one used the eigenphases and the eigenvectors of the bond scattering matrix $S(k)$. We considered graphs with Neumann and circular orthogonal ensemble (COE) boundary conditions. We show that in contrast to large Neumann graphs, for which the departure of many parameter-dependent spectral statistics from the random matrix theory (RMT) predictions is observed, for large COE graphs, the spectral statistics and IPR are in good agreement with the RMT predictions.

An analysis of thermomagnetic convection in a thin horizontal layer of magnetic fluid constrained horizontally by impermeable layers and subjected to a spatially and symmetrically modulated magnetic field is presented. The magnetic field as well as the temperature gradient are oriented vertically. For any nonzero magnetic field the base state is a convective one formed by a double vortex which reflects the symmetrical modulation. For long wave modulations the linear stability analysis reveals that the critical Rayleigh number ${\mathrm{Ra}}_c$ for the stability of the base state against small disturbances increases with increasing magnetic driving force. An analytical expression for ${\mathrm{Ra}}_c$ is derived which shows the characteristic feature of sudden jumps of ${\mathrm{Ra}}_c$ at particular values of the magnetic driving force.

At the microscale, even moderate temperature differences leading to thermal nonequilibrium can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Experimental measurements of the microscale Knudsen force have been reported by Passian et al., Phys. Rev. Lett. 90, 124503 (2003) using heated microcantilevers of atomic force microscope probes. The present study investigates the mechanism and magnitude of Knudsen forces in detail based on numerical solution of the Boltzmann kinetic equation with the ellipsoidal statistical Bhatnagar-Gross-Krook approximation for the collisional relaxation process. A direct comparison between the numerical simulations and experimental measurements is presented. We show that, assuming a fully diffuse interaction of gas molecules with the surfaces of the heated cantilever, simulations agree with measurements for different operating pressures in argon and nitrogen ambients. For the helium ambient the simulations agree with measurements only when an incomplete accommodation is used. A closed-form model for the nondimensional Knudsen force coefficient on a heated microbeam is obtained that can be used for quantifying such forces in analysis and design of microsystems under a wide range of geometrical, thermal, and pressure conditions.

We investigate the effect of a temperature gradient on oil recovery in a two-dimensional pore-network model. The oil viscosity depends on temperature as ${\mu }_o\propto e^{B/T}$, where $B$ is a physicochemical parameter, depending on the type of oil, and $T$ is the temperature. A temperature gradient is applied across the medium in the flow direction. Initially, the porous medium is saturated with oil, and then another fluid is injected. We have considered two cases representing different injection strategies. In the first case, the invading fluid viscosity is constant (finite viscosity ratio), while in the second one, the invading fluid is inviscid (infinite viscosity ratio). Our results show that for the case of finite viscosity ratio, recovery increases with $\Delta T$ independent of strength or sign of the gradient. For an infinite viscosity ratio, a positive temperature gradient is necessary to enhance recovery. Moreover, we show that for $\Delta T>0$, the percentage of oil recovery generally decreases (increases) with $B$ for a finite (infinite) viscosity ratio. Finally, we also extend our results for infinite viscosity ratio to a three-dimensional porous media geometry.

We explore whether vortex flows in the wake of a fixed circular cylinder can be stabilized using harmonic forcing. We use Föppl’s point vortex model augmented with a harmonic point source-sink mechanism which preserves conservation of mass and leaves the system Hamiltonian. We discover a region of Lyapunov-stable vortex motion for an appropriate selection of parameters. We identify four unique parameters that affect the stability of the vortices: the uniform flow velocity, vortex equilibrium positions, forcing amplitude, and forcing frequency. We assess the robustness of the controller using a Poincaré section.

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

The penetration of a projectile into a strongly coupled dusty plasma was studied in a radio-frequency discharge under microgravity conditions. A supersonic projectile produces an elongated dust-free cavity in its wake. The dynamics of the cavity is analyzed and compared with Langevin dynamics simulations. Besides a three-dimensional Mach cone structure, the simulation shows that the cavity dynamics can be subdivided into three phases: An opening phase with fixed time scale, a closing phase, whose duration is affected by the projectile speed and, finally, a phase of particle realignment in the target cloud, which persists for a long time after the closure of the cavity.

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions, whereas others do not.

We report small angle x-ray scattering (SAXS) studies of isotropic, nematic, and smectic mesophases formed by binary mixtures of bent-core (BC) and rod-shaped (RS) molecules. While optical studies indicate that the components are fully miscible, SAXS reveals fascinating structures that are consistent with segregation on a nanoscopic scale. We find that tilted smectic clusters, which have been previously reported in both the nematic and isotropic states of the pure BC materials, are also present in mixtures with up to 50 wt% of the RS compound; this is consistent with previous dielectric and flexoelectric studies on such mixtures. Unexpectedly in this concentration range the clusters are present in the isotropic and in the induced smectic phase range, as well as throughout the nematic phase. The results in the smectic phase also reveal complex layering phenomena, providing important insight into the interaction between bent and rod-shaped molecules. These studies will be crucial in the design of promising new functional nanomaterials.

Individuals often imitate each other to fall into the typical group, leading to a self-organized state of typical behaviors in a community. In this paper, we model self-organization in social tagging systems and illustrate the underlying interaction and dynamics. Specifically, we introduce a model in which individuals adjust their own tagging tendency to imitate the average tagging tendency. We found that when users are of low confidence, they tend to imitate others and lead to a self-organized state with active tagging. On the other hand, when users are of high confidence and are stubborn to change, tagging becomes inactive. We observe a phase transition at a critical level of user confidence when the system changes from one regime to the other. The distributions of post length obtained from the model are compared to real data, which show good agreement.

In the real world, there are many phenomena that are derived from deterministic systems but which fluctuate with nonuniform time intervals. This paper discusses the appropriate time scales that can be applied to such systems to analyze their properties. The financial markets are an example of such systems wherein price movements fluctuate with nonuniform time intervals. However, it is common to apply uniform time scales such as 1-min data and 1-h data to study price movements. This paper examines the validity of such time scales by using surrogate data tests to ascertain whether the deterministic properties of the original system can be identified from uniform sampled data. The results show that uniform time samplings are often inappropriate for nonlinear analyses. However, for other systems such as neural spikes and Internet traffic packets, which produce similar outputs, uniform time samplings are quite effective in extracting the system properties. Nevertheless, uniform samplings often generate overlapping data, which can cause false rejections of surrogate data tests.

Electrokinetic boundary conditions are derived for ac electrokinetic phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across a semiconductor-electrolyte interface (consisting of an electric double layer inside the electrolyte solution and a space charge layer inside the semiconductor) in an ac electric field with arbitrary wave forms. The presented electrokinetic boundary conditions allow for evaluation of the induced $\zeta$ potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Two well-known limiting cases, (i) the conventional insulating boundary condition and (ii) the perfectly polarizable boundary condition, can be recovered from the generalized electrokinetic boundary conditions derived in the present paper. Subsequently, we demonstrate the implementation of the derived boundary conditions for analyzing the ac induced-charge electrokinetic flow around a semiconducting cylinder. The results show that the flow circulations exist around the semiconducting cylinder and become stronger in the ac field with a lower frequency and around the semiconducting cylinder with a higher conductivity.

We investigate the forces exerted on embedded inclusions by a fluid medium with long-range correlations, described by an effective scalar field theory. Such forces are the basis for the medium-mediated Casimir-like force. To study these forces beyond thermal average, it is necessary to define them in each microstate of the medium. Two different definitions of these forces are currently used in the literature. We study the assumptions underlying them. We show that only the definition that uses the stress tensor of the medium gives the sought-after force exerted by the medium on an embedded inclusion. If a second inclusion is embedded in the medium, the thermal average of this force gives the usual Casimir-like force between the two inclusions. The other definition can be used in the different physical case of an object that interacts with the medium without being embedded in it. We show in a simple example that the two definitions yield different results for the variance of the Casimir-like force.

We study the physical mechanism of Maxwell’s demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule’s heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE’s efficiency is evaluated in detail to prove the validity of the second law of thermodynamics.

We report results of calorimetric studies for the binary mixture of rodlike host $n$-alkyloxy-cyanobiphenyl ($n$OCB, $n=8,9$) and bent-shaped guest 1,3-phenylene-bis[4-(3-methylbenzoyloxy)]-4${}^{\text{'}}$-$n$-dodecylbiphenyl-4${}^{\text{'}}$-carboxylate (BC12). The effect of bent-shaped dopant molecules on the critical behavior associated with the nematic-smectic-$A_d$ phase transition has been studied in detail. The transition temperature for the nematic-smectic-$A_d$ phase sharply decreases as the increase of the mole fraction of the dopant concentration (denoted $X$ for the BC12/9OCB mixture and $Y$ for the BC12/8OCB mixture). The dependence of the critical exponent $\alpha$ on $X$ and $Y$ is well explained in terms of the McMillan ratio. A nearly tricritical exponent has been obtained for the $X=0.01$ mixture. $X=0.02-0.03$ mixtures, pure 8OCB, and $Y=0.01-0.03$ mixtures exhibit nonuniversal behaviors with effective exponents lying between the 3D-$\mathit{XY}$ and tricritical exponents. The heat capacity anomaly for $Y=0.05$ has been well described with the 3D-$\mathit{XY}$ exponent. The critical amplitude ratio $A^{-}/A^{+}$ is close to $1$ and insensitive to the dopant concentration. No Fisher renormalization of the critical exponent has been observed even for nearly tricritical compositions, which indicates the smallness of the concentration plays a decisive role rather than the steepness of the $N$-Sm$A_d$ phase boundary.

By making use of the developed potential theory, we investigate the polymer-mediated depletion interactions between nanoparticles and hard planar surfaces in the following settings: (i) interaction between two nanoparticles; (ii) interactions between nanoparticle and hard planar surface; (iii) interaction between two nanoparticles in the presence of hard planar surface; and (iv) interaction between nanoparticle and walls of the plane-parallel slab. For each of the listed systems, we have calculated the polymer end density, excess grand potential, and the potential of the depletion forces. On the basis of the obtained results, we have analyzed the effect of the geometric constraints imposed by hard walls on the polymer density structure and the depletion interaction between nanoparticles.

Stochastic resonance (SR) enhanced by time-delayed feedback control is studied. The system in the absence of control is described by a Langevin equation for a bistable system, and possesses a usual SR response. The control with the feedback loop, the delay time of which equals to one-half of the period ($2\pi /\Omega$) of the input signal, gives rise to a noise-induced oscillatory switching cycle between two states in the output time series, while its average frequency is just smaller than $\Omega$ in a small noise regime. As the noise intensity $D$ approaches an appropriate level, the noise constructively works to adapt the frequency of the switching cycle to $\Omega$, and this changes the dynamics into a state wherein the phase of the output signal is entrained to that of the input signal from its phase slipped state. The behavior is characterized by power loss of the external signal or response function. This paper deals with the response function based on a dichotomic model. A method of delay-coordinate series expansion, which reduces a non-Markovian transition probability flux to a series of memory fluxes on a discrete delay-coordinate system, is proposed. Its primitive implementation suggests that the method can be a potential tool for a systematic analysis of SR phenomenon with delayed feedback loop. We show that a $D$-dependent behavior of poles of a finite Laplace transform of the response function qualitatively characterizes the structure of the power loss, and we also show analytical results for the correlation function and the power spectral density.