Topological analysis is employed for the first time to our knowledge as a method of validation for a physical model describing a chaotic system. Topological analysis theory provides both a way to characterize the topological structure of chaotic attractors by means of a set of integer numbers and a method to obtain this set departing from a time series generated by the chaotic system. The validation method proposed here consists of comparing the topological structure of chaotic attractors obtained from time series generated on the one hand by an experimental system and on the other hand by the numerical model under test. This procedure has been applied to an erbium-doped fiber laser subject to pump power sine-wave modulation.

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

A sharp-interface immersed boundary lattice Boltzmann method (IBLBM) is developed to reduce spurious-pressure oscillations in moving boundary problems. We adopt a cut-cell-based method, i.e., the partially saturated computational cell method, because the primary cause of spurious-pressure oscillations is the failure to obey the geometric conservation law near the boundary in the sharp-interface IBLBM. We modify a sharp-interface IBLBM (ghost fluid method) to fit the cut-cell approach. This boundary condition can guarantee the Dirichlet and Neumann boundary conditions for velocity and pressure. Some simulations are shown to test the validity of the method, including a circular cylinder with motions that are at rest, moving, oscillatory, and neutrally buoyant. The results illustrate that the method reduces effectively spurious pressure and can simulate moving boundary problems, especially when pressure field accuracy is a key concern.

The Burnett coefficient $B$ is investigated for transport in one-dimensional quantum many-body systems. Extensive numerical computations in spin-$1/2$ chains suggest a linear growth with time, $B\left(t\right)\sim t$, for nonintegrable chains exhibiting diffusive transport. For integrable spin chains in the metallic regime, on the other hand, we find a cubic growth with time, $B\left(t\right)\sim -D_{\mathrm{m}}^2{t}^3$, with the proportionality constant being simply a square of the Drude weight $D_{\mathrm{m}}$. The results are corroborated with additional studies in noninteracting quantum chains and in the classical limit of large-spin chains.

Advances in precise focusing of colloidal particles in microfluidic systems open up the possibility of using microfluidic junctions for particle separation and filtering applications. We present a comprehensive numerical study of the dynamics of solid and porous microparticles in T-shaped junctions. Good agreement with experimental data is obtained on the location of particle-separating streamlines for single solid particles with realistic parameters corresponding to the experiments. We quantify the changes in the position of the separating line for porous, partially penetrable colloids. A prediction of the full phase diagram for particle separation is presented in the case of two successive particles entering a T-junction. Our results suggest the intriguing possibility of using the one- and two-particle T-junctions as logic gates.

Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.

We use Monte Carlo and transfer matrix methods in combination with extrapolation schemes to determine the phase diagram of the two-dimensional superantiferromagnetic (SAF) Ising model with next-nearest-neighbor (NNN) interactions in a magnetic field. The interactions between nearest-neighbor (NN) spins are ferromagnetic along $x$, and antiferromagnetic along $Y$. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of second-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with reentrant behavior. The NNN couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio $R_c=\frac{1}{2}$ between NNN and NN couplings, beyond which the SAF phase no longer exists.

By combining a measurable vapor-liquid coexistence curve and the extended van der Waals-type of equation of state (EOS) with the additional temperature-dependent coefficient, the phenomenological model of global fluid asymmetry has been developed separately for both coexisting bulk phases in the entire range of subcritical states. It is shown, in particular, that the adequate description of a liquid branch and its near-critical vicinity in terms of appropriate critical exponents and amplitudes connected by the two-scale-factor universal interrelations can be achieved. The asymmetric influence of heterophase fluctuations on the criticality of gaseous states is demonstrated. It is inherently similar to the well-known Fisher's droplet model, which corresponds to the scaling EOS too. The principle of corresponding isotherms has been formulated without any adjustable parameters. An attempt to avoid the use of a locally singular coexistence-curve diameter is proposed in the framework of two alternative models. The accurate vapor-liquid data for two fluid metals, Rb and Cs, as well as two molecular fluids, C${}_2$H${}_6$ and CO${}_2$, are reanalyzed by the above models to confirm the presumed opportunity.

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.

We study the three-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method. On the basis of these stationary points, we analyze the complexity and other quantities related to the glass transition of the model and compare these finite-system quantities to their exact counterparts in the thermodynamic limit.

We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis et al. [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity $\langle \omega \rangle \sim v_0^3$, and (ii) frequent collisions (FC), with $\langle \omega \rangle \sim v_0$. We also study the fluctuations of the angle spanned in a large-time interval $\Delta \theta$, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.

Multicomponent diffusional mechanisms in the ternary LiCl-KCl system are elucidated using the Green-Kubo formalism and equilibrium molecular dynamics simulations. The Maxwell-Stefan (MS) diffusion matrix is evaluated from the Onsager dynamical matrix that contains the diffusion flux correlation functions. From the temporal behavior of the correlation functions, we observe that the Li-Li and Li-Cl ion pairs have a pronounced cage dynamics that remains noticeably strong even at high temperatures. Even though the Onsager coefficients, which are the time integrals of the diffusion flux correlation functions, portray a relatively smooth variation across various compositions and temperatures, we observe a sign change and a divergent-like behavior for the MS diffusivity of the K-Li ion pair at a temperature of $\sim$1100 K for the eutectic composition, and at a KCl mole fraction of $\sim$0.49 at 1043 K. Negative MS diffusivities, while unusual, are however shown to satisfy the nonnegative entropic constraints.

The ordering transitions of a two-dimensional lattice liquid characterized by a single favored local structure (FLS) are studied using Monte Carlo simulations. All eight distinct geometries for the FLS are considered and we find a variety of ordering transitions: first order, continuous, and multistep transitions. Using an entropy-energy representation of the freezing transition we resolve the dual influence of the local structure on the ordering transition, i.e., via the energy of the crystal and the entropy cost of structure in the liquid.

Optical methods are most convenient for analyzing spatially periodic patterns with wave vector $\mathit{q}$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a “short” wavelength $\lambda \ll 2\pi /q$ passes the nematic layer. Recording the transmitted light the patterns are either directly visualized by shadowgraphy or characterized more indirectly by the diffraction fringes due to the optical-grating effects of the pattern. In this work we present a systematic short-wavelength analysis of these methods for the commonly used planar orientation of the optical axis of liquid crystal at the confining surfaces. Our approach covers general three-dimensional experimental geometries with respect to the relative orientation of $\mathit{q}$ and of the wave vector $\mathit{k}$ of the incident light. In particular, we emphasize the importance of phase-grating effects, which are not accessible in a pure geometric optics approach. Finally, as a by-product we present also an optical analysis of convection rolls in Rayleigh-Bénard convection, where the refraction index of the fluid is isotropic in contrast to its uniaxial symmetry in nematic liquid crystals. Our analysis is in excellent agreement with an earlier physical optics approach by Trainoff and Cannell [Phys. Fluids 14, 1340 (2002)], which is restricted to a two-dimensional geometry and technically much more demanding.

The cross-bridge power-stroke model has been widely used to describe the motion of large motor assemblies connected to a common rigid filament. In this paper, we go beyond the original velocity-ensemble approach and propose a master equation approach to account for the cooperative motion of a finite number of motors based on the cross-bridge model. By studying the force-velocity relationship for motors with strain-independent detachment rate, we show the convergence of our approach to the velocity-ensemble approach in the limit of large motor numbers. In the case that the detachment rate of motors is strain dependent, based on two assumptions for the strain distribution among motors, we show the occurrence of the bimodal distribution of the number of motors bound to the filament. This provides a new perspective to look at the instability of a multimotor system, which is essential for all the experimentally observed complex motions displayed by a group of motors, such as hysteresis, bidirectional motion, and spontaneous oscillation. By comparing the velocities calculated using the two assumptions with the stochastic simulation, it suggests that the coupling between motors via the common connection to the filament might facilitate the fast movement of filaments at small loading forces.

Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise interactions originate from multiway interactions, by starting from ensembles of hypergraphs and applying projections that generate ensembles of weighted projected networks. I calculate analytically the statistical properties of weighted projected networks, and suggest ways these could be used beyond theoretical studies. Weighted projected networks typically exhibit weight disorder along links even for very simple generating hypergraph ensembles. Also, as the size of a hypergraph changes, a signature of multiway interaction emerges on the link weights of weighted projected networks that distinguishes them from fundamentally weighted pairwise networks. This signature could be used to search for hidden multiway interactions in weighted network data. I find the percolation threshold and size of the largest component for hypergraphs of arbitrary uniform rank, translate the results into projected networks, and show that the transition is second order. This general approach to network formation has the potential to shed new light on our understanding of weighted networks.

Self-recovery of function is one of the remarkable properties of biological systems, and its implementation in autonomous distributed systems is highly desirable. In this study, we propose an autonomous distributed system which is capable of searching for closed loops in a network in which nodes are connected by unidirectional paths. A closed loop is defined as a phase synchronization of a group of oscillators belonging to the corresponding nodes. In addition, to develop a system capable of self-recovery (the ability to find a loop when one of the connections in the existing loop is suddenly removed), we have developed regulatory rules for the interaction between nodes. These rules are used to construct a regulation network in which the stability of nodes and that of loops are mutually sustained, allowing the system to function as a loop-searching system with self-recovery properties.

Based on the theory of shape instability and diffusive instability for single bubbles, we have studied the instability of an individual bubble in a bubble chain and found that its stable area enlarges the narrower the distance between bubbles. The spatial stability of the bubble chain is due to the secondary Bjerknes force between bubbles. Numerical calculations show the tension of the bubble chain varies with bubble distance and maxima appear at certain distances which could correspond to the stable states of the bubble chain.

The Langmuir oscillations, Landau damping, and growing unstable modes in an electron-positron (EP) plasma are studied by using the Vlasov and Poisson's equations in the context of the Tsallis's nonextensive statistics. Logically, the properties of the Langmuir oscillations in a nonextensive EP plasma are remarkably modified in comparison with that of discussed in the Boltzmann-Gibbs statistics, i.e., the Maxwellian plasmas, because of the system under consideration is essentially a plasma system in a nonequilibrium stationary state with inhomogeneous temperature. It is found that by decreasing the nonextensivity index $q$ which corresponds to a plasma with excess superthermal particles, the phase velocity of the Langmuir waves increases. In particular, depend on the degree of nonextensivity, both of damped and growing oscillations are predicted in a collisionless EP plasma, arise from a resonance phenomena between the wave and the nonthermal particles of the system. Here, the mechanism leads to the unstable modes is established in the context of the nonextensive formalism yet the damping mechanism is the same developed by Landau. Furthermore, our results have the flexibility to reduce to the solutions of an equilibrium Maxwellian EP plasma (extensive limit $q\to 1$), in which the Langmuir waves are only the Landau damped modes.

In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter ${\gamma }_1$, denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by ${\gamma }_1$ are discussed in detail.