Energetic deuterium ions from large deuterium clusters $(>10\mathrm{nm}$ diameter) irradiated by an intense laser pulse $(>{10}^{16}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2)$ produce DD fusion neutrons for a time interval determined by the geometry of the resulting fusion plasma. We present an analytical solution of this time interval, the plasma disassembly time, for deuterium plasmas that are cylindrical in shape. Assuming a symmetrically expanding deuterium plasma, we calculate the expected fusion neutron yield and compare with an independent calculation of the yield using the concept of a finite confinement time at a fixed plasma density. The calculated neutron yields agree quantitatively with the available experimental data. Our one-dimensional simulations indicate that one could expect a tenfold increase in total neutron yield by magnetically confining a $10\text{−}\mathrm{keV}$ deuterium fusion plasma for $10\mathrm{ns}$.

In contrast to most real fluids, angular momentum is not a locally conserved quantity in some mesoscopic simulation methods. Here we quantify the importance of this conservation in the flow fields associated with different colloidal systems. The flow field is analytically calculated with and without angular momentum conservation for the multiparticle collision dynamics (MPC) method, and simulations are performed to verify the predictions. The flow field generated around a colloidal particle moving under an external force with slip boundary conditions depends on the conservation of angular momentum, and the amplitude of the friction force is substantially affected. Interestingly, no dependence on the angular momentum conservation is found for the flow fields generated around colloids under the influence of phoretic forces. Moreover, circular Couette flow between a no-slip and a slip cylinder is investigated, which allows us to validate one of the two existing expressions for the MPC stress tensor.

Nematic samples filling a flat cell or the annular region between two concentric cylinders with hybrid anchoring conditions at the boundaries are investigated by setting up and minimizing their Frank elastic free energy. The coupling with the surfaces is taken to be strong on one side and weak on the other. The equations are numerically solved and the conditions for which the molecular organization inside the cell becomes uniform are analyzed. The classical calculation performed by G. Barbero and R. Barberi [J. Phys. 44, 609 (1983)] is reproduced and investigated from a different point of view, in order to compare the results of planar and cylindrical geometries. The results suggest that the cylindrical cell presents some unusual features deserving a more complete investigation. Although most part of the transitional phenomena are found for $K_{11}>K_{33}$, a case not common for ordinary (lyotropic and thermotropic) liquid crystals, it is possible to find a completely uniform cell even for $K_{11}<K_{33}$ in both the geometries considered here.

When encountering a hostile particle, the avoidance behaviors of the vortex state of self-propelled particles exhibit phase transition phenomena such that the vortex state can change into a crystal state. Based on the self-propelled particle model and a molecular dynamics simulation, the dynamic response of the vortex swarm induced by a hostile particle (predator or obstacle) is studied. Three parameters are defined to characterize the collective escaping behaviors, including the order parameter, the flock size, and the roundness parameter. If a predator moves slower with a larger risk radius, the vortex swarm cannot return to its original vortex state, but rather transforms into a crystal state. The critical phase transition radius, the maximum risk radius of a predator with which the transition from a vortex to crystal state cannot take place, is also examined by considering the influence of the model parameters. To some degree, the critical radius reflects the stability and robustness of the vortex swarm.

In recent years, the competition between randomness and nonlinearity was extensively explored. In the present paper, the dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In the absence of the random potential, it is an integrable model and the solitons are stable. As a result of the random potential, this stability is destroyed. In a certain regime, for short times, particlelike dynamics with constant mass is found; in another regime, particlelike dynamics with varying mass takes place. In particular, an effective potential is found that predicts correctly changes in the direction of motion of the soliton. This potential is a scaling function of time and strength of the potential, leading to a relation between the first time when the soliton changes direction and the strength of the random potential.

This work is inspired by the expansion of the plasma bubble in a narrow gap reported by Chu and Lee [Phys. Rev. Lett. 107, 225001 (2011)]. We report the unstable phenomena of the plasma-liquid interface with different curvature in a Hele-Shaw cell. Dielectric barrier discharge is produced in the cell at atmospheric pressure which is partially filled with silicone oil. We show that the Saffman-Taylor-like instability is observed on the bubble-type, channel-type, and drop-type interfaces. The Schlieren observation of the plasma-drop interaction reveals that there is a vapor layer around the drop and the particle image velocimetry shows the liquid flow inside the drop. We propose that the thermal Marangoni effect induced by the plasma heating is responsible for the unstable phenomena of the plasma-liquid interaction. The fluctuation of the interface is shown consistently with the Saffman-Taylor instability modified by the temperature-dependent velocity and surface tension.

Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials.

Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.

A Fermi accelerator is a billiard with oscillating walls. A leaky accelerator interacts with an environment of an ideal gas at equilibrium by exchange of particles through a small hole on its boundary. Such interaction may heat the gas: we estimate the net energy flow through the hole under the assumption that the particles inside the billiard do not collide with each other and remain in the accelerator for a sufficiently long time. The heat production is found to depend strongly on the type of Fermi accelerator. An ergodic accelerator, i.e., one that has a single ergodic component, produces a weaker energy flow than a multicomponent accelerator. Specifically, in the ergodic case the energy gain is independent of the hole size, whereas in the multicomponent case the energy flow may be significantly increased by shrinking the hole size.

We experimentally investigated the temperature dependence of intensity of single-bubble sonoluminescence (SBSL) in 85 wt %. sulfuric acid. It was found that the intensity increases as temperature increases from 15 °C and 25 °C, confirming what has been predicted by A. Moshaii et al. [Phys. Rev. E 84, 046301 (2011)] theoretically. This behavior, however, is completely opposite to what has been observed for water. Above 25 °C, the behavior of intensity of SBSL in sulfuric acid is found to be independent of the liquid temperature. Moreover, it was observed that as the temperature increases, contribution to total intensity from the UV portion of the spectrum increases while contribution from the visible portion decreases, indicating higher bubble temperatures at higher liquid temperatures. Results of this experiment further indicate that the intensity threshold at each temperature is not determined by the shape or the positional stability conditions but by the driving pressure at which the transition from SBSL to multibubble sonoluminescence (MBSL) takes place.

Water's density maximum at $4{}^{\circ }\mathrm{C}$ makes it well suited to study internal gravity wave excitation by convection: an increasing temperature profile is unstable to convection below $4{}^{\circ }\mathrm{C}$, but stably stratified above $4{}^{\circ }\mathrm{C}$. We present numerical simulations of a waterlike fluid near its density maximum in a two-dimensional domain. We successfully model the damping of waves in the simulations using linear theory, provided we do not take the weak damping limit typically used in the literature. To isolate the physical mechanism exciting internal waves, we use the spectral code dedalus to run several simplified model simulations of our more detailed simulation. We use data from the full simulation as source terms in two simplified models of internal-wave excitation by convection: bulk excitation by convective Reynolds stresses, and interface forcing via the mechanical oscillator effect. We find excellent agreement between the waves generated in the full simulation and the simplified simulation implementing the bulk excitation mechanism. The interface forcing simulations overexcite high-frequency waves because they assume the excitation is by the “impulsive” penetration of plumes, which spreads energy to high frequencies. However, we find that the real excitation is instead by the “sweeping” motion of plumes parallel to the interface. Our results imply that the bulk excitation mechanism is a very accurate heuristic for internal-wave generation by convection.

A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to the distribution of fragments. The resulting power law directly leads to Benford's law for the first digits of the parts.

We present the exact closed-form expression for the partition function of a dimer model on a generalized finite checkerboard rectangular lattice under periodic boundary conditions. We investigate three different sets of dimer weights, each with different critical behaviors. We then consider different limits for the model on the three lattices. In one limit, the model for each of the three lattices is reduced to the dimer model on a rectangular lattice, which belongs to the $c=-2$ universality class. In another limit, two of the lattices reduce to the anisotropic Kasteleyn model on a honeycomb lattice, the universality class of which is given by $c=1$. The result that the dimer model on a generalized checkerboard rectangular lattice can manifest different critical behaviors is consistent with early studies in the thermodynamic limit and also provides insight into corrections to scaling arising from the finite-size versions of the model.

We present a comprehensive study of the two-dimensional one-component plasma in the cell model with charged boundaries. Starting from weak couplings through a convenient approximation of the interacting potential we were able to obtain an analytic formulation to the problem deriving the partition function, density profile, contact densities, and integrated profiles that compared well with the numerical data from Monte Carlo simulations. Additionally, we derived the exact solution for the special cases of $\mathrm{\Xi }=1,2,3,\cdots$, finding a correspondence between those from weak couplings and the latter. Furthermore, we investigated the strong-coupling regime taking into consideration the Wigner formulation. Elaborating on this, we obtained the profile to leading order, computed the contact density values as compared to those derived in an earlier work on the contact theorem. We formulated adequately the strong-coupling regime for this system that differed from previous formulations. Ultimately, we calculated the first-order corrections and compared them against numerical results from our simulations with very good agreement; these results compared equally well in the planar limit, whose results are well known.

We have studied the dynamic phase transition (DPT) of the kinetic Ising model in systems with surfaces within the mean-field approximation. Varying the surface exchange coupling strength $J_s$, the amplitude of the externally applied oscillating field $h_0$, and its period $P$, we explore the dynamic behavior of the layer-dependent magnetization and the associated DPTs. The surface phase diagram shows several features that resemble those of the equilibrium case, with an extraordinary bulk transition and a surface transition for high $J_s$ values, independent from the value of $h_0$. For low $J_s$, however, $h_0$ is found to be a crucial parameter that leads to nonuniversal surface behavior at the ordinary bulk transition point. Specifically, we observed here a bulk-supported surface DPT for high field amplitudes $h_0$ and correspondingly short critical periods $P_c$, whereas this surface transition simultaneous to the bulk one is suppressed for slow critical dynamics occurring for low values of $h_0$. The suppression of the DPT for low $h_0$ not only occurs for the topmost surface layer, but also affects a significant number of subsurface layers. We find that the key physical quantity that explains this nonuniversal behavior is the time correlation between the dynamic surface and bulk magnetizations at the bulk critical point. This time correlation has to pass a threshold value to trigger a bulk-induced DPT in the surface layers. Otherwise, dynamic phase transitions are absent at the surface in stark contrast to the equilibrium behavior of the corresponding thermodynamic Ising model. Also, we have analyzed the penetration depth of the dynamically ordered phase for the surface DPT that occurs for large $J_s$ values. Here we find that the penetration depth depends strongly on $J_s$ and behaves identically to the corresponding equilibrium Ising model.

It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.

In studying fundamental physical limits and properties of computational processes, one is faced with the challenges of interpreting primitive information-processing functions through well-defined information-theoretic as well as thermodynamic quantities. In particular, transfer entropy, characterizing the function of computational transmission and its predictability, is known to peak near critical regimes. We focus on a thermodynamic interpretation of transfer entropy aiming to explain the underlying critical behavior by associating information flows intrinsic to computational transmission with particular physical fluxes. Specifically, in isothermal systems near thermodynamic equilibrium, the gradient of the average transfer entropy is shown to be dynamically related to Fisher information and the curvature of system's entropy. This relationship explicitly connects the predictability, sensitivity, and uncertainty of computational processes intrinsic to complex systems and allows us to consider thermodynamic interpretations of several important extreme cases and trade-offs.

Two-dimensional (2D) nuclear magnetic resonance (NMR) experiments involve a sequence of longitudinal ($T_1$) and transverse ($T_2$) measurements. In a previous paper we showed that if each of these 1D measurements can be represented by two exponential decays then there can be an accurate analytic solution for the 2D measurements with no additional information. In this paper we extend the theory to the case where there are three decay channels for the 1D measurements. The resulting analytic theory introduces a single free parameter, which is a rotation angle in the vector space spanned by the normal modes. Our predictions agree quite well with numerical results based on the microporous grain consolidation ($\mu \text{GC}$) model. The theory allows one to deduce information about decay modes in situations in which they may not be measurable in a conventional 1D measurement because the amplitude of that mode is too small.