The spin-glass Blume-Capel model is studied by using an extended mean-field renormalization group approximation. The effects of a probability distribution of the bilinear interaction coupling with competing interactions have been investigated. The phase diagrams show second-order phase boundaries among ferromagnetic, antiferromagnetic, paramagnetic, and spin-glass phases. On the other hand, tricritical phenomena exist only for certain values of the concentration of ferromagnetic bonds as well as ratios of the ferromagnetic to the antiferromagnetic competitive interactions. An application to the magnetic properties of ternary system Fe-Al-Mn alloys is presented. Good fittings to the experimental data are obtained.

The lattice Green's functions (LGFs) and density of states (DOS) for noninteracting models on three related lattices are presented. The DOS and LGFs at the origin for the kagome and diced lattices are rederived. Furthermore, from the form obtained for the DOS of the hyperkagome lattice, it seems highly suggestive that a closed form expression can be obtained if a particular complicated yet highly symmetrical integral can be solved. The results have been checked numerically. The continuum of energy states in the hyperkagome lattice and the appearance of a zero in the kagome lattice may be explicitly seen from the formulas obtained.

A generalization of the Faxén's theorem to the nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow is presented. From this result, expressions for the velocity autocorrelation function (VAF) and the time-dependent diffusion coefficient of the particle can be obtained. We analyze the behavior of the VAF and the time-dependent diffusion coefficient for different physical regimes of the suspending fluid. The relevance of the theorem to microrheology is discussed.

The structural changes of a two-dimensional colloidal crystal, consisting of glycerol droplets on a nematic liquid-crystal surface, due to a magnetic field applied parallel to the liquid-crystal surface, were observed and analyzed. The hexagonal lattice arrangement of glycerol droplets transformed into a smaller, anisotropic hexagonal-like lattice when the magnetic field was applied. The intermediate stage of the transition is influenced by the way in which the magnetic field is applied. When a sufficiently strong magnetic field is applied directly, the transition proceeds by passing through a random arrangement and then through a chainlike arrangement. With a gradually increasing magnetic field, the transition starts locally and extends throughout the entire region. The relaxation processes that occur once the field is switched off are very similar, irrespective of the manner in which the field is switched off. The relaxation begins at the outside and then extends to the central regions. No tendency to form a chainlike arrangement was observed during the relaxation process. The processes during switching on and off demonstrate a hysteresis with respect to the magnetic field strength.

It is well known that during homology recognition and strand exchange the double-stranded DNA (dsDNA) in DNA/RecA filaments is highly extended, but the functional role of the extension has been unclear. We present an analytical model that calculates the distribution of tension in the extended dsDNA during strand exchange. The model suggests that the binding of additional dsDNA base pairs to the DNA/RecA filament alters the tension in dsDNA that was already bound to the filament, resulting in a nonlinear increase in the mechanical energy as a function of the number of bound base pairs. This collective mechanical response may promote homology stringency and underlie unexplained experimental results.

We show evidence of the frozen dynamics (Kibble-Zurek mechanism) at the transition one-dimensional (1D) front of an extended 1D array of convective oscillators that undergo a secondary subcritical bifurcation. Results correspond to a global synchronization process from nonlocal coupling between the oscillating units. The quenched dynamics exhibits defect trapping at the synchronization front according to the Kibble-Zurek mechanism, predicted for condensed matter systems. A stronger subcriticality prevents the fronts from freezing defects during the quenched transitions. A synchronization model of supercritical oscillating units is proposed to explain differentiation mechanisms in morphogenesis above a critical crossing rate when the frequency of the individual oscillators becomes coherent. The phases of such oscillators are spatially coupled through a Kuramoto-Battogtokh term that leads to the experimentally observed subcriticality. As a consequence, we show that the Kibble-Zurek mechanism overcomes non-locality of a geometrical network above a critical crossing rate.

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong-coupling theories and molecular dynamics simulation to quantum systems at strong coupling. The correspondence is made at the level of the grand-canonical ensembles for the two systems. An effective temperature, local chemical potential, and pair potential are introduced to define the corresponding classical system. These are determined formally by requiring the equivalence of the grand potentials and their functional derivatives. Practical inversions of these formal definitions are indicated via the integral equations for densities and pair correlation functions of classical liquid theory. Application to the ideal Fermi gas is demonstrated, and the weak-coupling form for the pair potential is given. In a companion paper two applications are described: the thermodynamics and structure of uniform jellium over a range of temperatures and densities and the shell structure of harmonically bound charges.

In the preceding paper, the structure and thermodynamics of a given quantum system was represented by a corresponding classical system having an effective temperature, local chemical potential, and pair potential. Here, that formal correspondence is implemented approximately for applications to two quantum systems. The first is the electron gas (jellium) over a range of temperatures and densities. The second is an investigation of quantum effects on shell structure for charges confined by a harmonic potential.

We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length $k$ on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for $k=7$. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale ${\xi }^{*}\gtrsim 1400$ on the square lattice. For distances smaller than ${\xi }^{*}$, correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we can not rule out a crossover to Ising universality class at length scales $\gg {\xi }^{*}$. On the triangular lattice, the critical exponents are consistent with those of the two-dimensional three-state Potts universality class.

Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Lévy stable distribution. If this distribution is truncated, the covariance can be derived in the limit of large time; it falls exponentially. Covariance in the stable case, studied for the Cauchy distribution, exhibits a weakly stretched exponential shape and can be approximated by the simple exponential. The dependence of that function on system parameters is determined. Then we consider a dynamics which involves the above process and obeys the generalized Langevin equation, the same as for the Gaussian case. The resulting distributions possess power-law tails, which fall similarly to those for the driving noise, whereas central parts can assume the Gaussian shape. Moreover, a process with the covariance $1/t$ at large time is constructed, and the corresponding dynamical equation is solved. Diffusion properties of systems for both covariances are discussed.

We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding $\beta$ functions to a universal canonical form, valid to all perturbative orders. Then we determine the asymptotic solutions of the RG equations in various critical regimes: the infinite-volume critical behavior in the disordered phase, the finite-size scaling limit for homogeneous systems of finite size, and the trap-size scaling limit occurring in two-dimensional bosonic particle systems trapped by an external space-dependent potential.

We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations, we explore a special case in which the natural frequencies of the oscillators and the vertex degrees are linearly coupled. We find that in uncorrelated scale-free networks with the degree distribution exponent $2<\gamma <3$, the model undergoes a first-order phase transition, while the transition becomes second order at $\gamma >3$. If $\gamma =3$, the phase synchronization emerges as a result of a hybrid phase transition that combines an abrupt emergence of synchronization, as in first-order phase transitions, and a critical singularity, as in second-order phase transitions. The critical fluctuations manifest themselves as avalanches in the synchronization process. Comparing our analytical calculations with numerical simulations for Erdős-Rényi and scale-free networks, we demonstrate that the annealed network approach is accurate if the mean degree and size of the network are sufficiently large. We also study analytically and numerically the Kuramoto model on star graphs and find that if the natural frequency of the central oscillator is sufficiently large in comparison to the average frequency of its neighbors, then synchronization emerges as a result of a first-order phase transition. This shows that oscillators sitting at hubs in a network may generate a discontinuous synchronization transition.

The transport coefficients of a granular fluid driven by a stochastic bath with friction are obtained by solving the inelastic Enskog kinetic equation from the Chapman-Enskog method. The heat and momentum fluxes as well as the cooling rate are determined to first order in the deviations of the hydrodynamic field gradients from their values in the homogeneous steady state. Since the collisional cooling cannot be compensated locally for the heat produced by the external driving force, the reference distribution $f^{\left(0\right)}$ (zeroth-order approximation) depends on time through its dependence on temperature. This fact gives rise to conceptual and practical difficulties not present in the undriven case. On the other hand, to simplify the analysis and given that we are interested in computing transport in the first order of deviations from the reference state, the steady-state conditions are considered to get explicit forms for the transport coefficients and the cooling rate. A comparison with recent Langevin dynamics simulations for driven granular fluids shows an excellent agreement for the kinematic viscosity although some discrepancies are observed for the longitudinal viscosity and the thermal diffusivity at large densities. Finally, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state is performed. As expected, no instabilities are found thanks to the presence of the external bath.

We study the interactions of submicrometer diameter silica particles, surface functionalized with DMOAP (N,N-dimethyl-n-octadecyl-3-aminopropyl-trimethoxysilyl chloride), in the nematic liquid crystal 5CB (pentylcyanobiphenil). Using the methods of video-tracking dark-field microscopy, we have measured the pair-binding energy of 35- to 450-nm-diameter silica particles, which is in the range between 100 and 1000 $k_{B}T$. It is therefore high enough for the formation of thermally stable nanocolloidal pairs of 35 nm diameter. We find that smaller colloids with the diameter around 22 nm do not form thermally stable pairs, which seems to be currently the lower limit for nanocolloidal assembly in the nematic liquid crystals. We also study the particle interactions with point and Saturn-ring defects and discuss the possibility of hierarchical structures generated by particles of different sizes assembled by topological defects.

Radiopharmaceuticals emitting Auger electrons are often injected into patients undergoing cancer treatment with targeted radionuclide therapy (TRT). In this type of radiotherapy, the radiation source is radial and most of the emitted primary particles are low-energy electrons (LEEs) having kinetic energies distributed mostly from zero to a few hundred electron volts with very short ranges in biological media. These LEEs generate a high density of energy deposits and clustered damage, thus offering a relative biological effectiveness comparable to that of alpha particles. In this paper, we present a simple model and corresponding measurements to assess the energy deposited near the site of the radiopharmaceuticals in TRT. As an example, a calculation is performed for the decay of a single ${}^{125}$I radionuclide surrounded by a 1-nm-radius spherical shell of cytosine molecules using the energy spectrum of LEEs emitted by ${}^{125}$I along with their stopping cross sections between 0 and 18 eV. The dose absorbed by the cytosine shell, which occupies a volume of 4 nm${}^3$, is extremely high. It amounts to 79 kGy per decay of which 3$\%$, 39$\%$, and 58$\%$ is attributed to vibrational excitations, electronic excitations, and ionization processes, respectively.

We investigate the occurrence of quasisynchronous events in a random network of excitatory leaky integrate-and-fire neurons equipped with short-term plasticity. The dynamics is analyzed by monitoring both the evolution of global synaptic variables and, on a microscopic ground, the interspike intervals of the individual neurons. We find that quasisynchronous events are the result of a mixture of synchronized and unsynchronized motion, analogously to the emergence of synchronization in the Kuramoto model. In the present context, disorder is due to the random structure of the network and thereby vanishes for a diverging network size $N$ (i.e., in the thermodynamic limit), when statistical fluctuations become negligible. Remarkably, the fraction of asynchronous neurons remains strictly larger than zero for arbitrarily large $N$. This is due to the presence of a robust homoclinic cycle in the self-generated synchronous dynamics. The nontrivial large-$N$ behavior is confirmed by the anomalous scaling of the maximum Lyapunov exponent, which is strictly positive in a finite network and decreases as $N^{-0.27}$. Finally, we have checked the robustness of this dynamical phase with respect to the addition of noise, applied to either the reset potential or the leaky current.

We study the dynamics of nonwetting liquid blobs during immiscible two-phase flows in stochastically reconstructed porous domains predominantly saturated by a wetting fluid. The flow problem is solved explicitly using a Lattice-Boltzmann model that captures both the bulk phase and interfacial dynamics of the process. We show that the nonwetting blobs undergo a continuous life cycle of dynamic breaking up and coalescence producing two populations of blobs, a mobile and a stranded one, that exchange continuously mass between them. The process reaches a “steady state” when the rates of coalescence and breaking up become equal, and the macroscopic flow variables remain practically constant with time. At steady state, mass partitioning between mobile and immobile populations depends strongly on the applied Bond number $\mathrm{Bo}$ and the initial nonwetting phase distributions. Three flow regimes are identified: a single-phase flow Darcy-type regime at low $\mathrm{Bo}$ numbers, a non-Darcy two-phase flow regime at intermediate values of $\mathrm{Bo}$, where the capillary number scales as $\mathrm{Ca}\propto {\mathrm{Bo}}^2$, and a Darcy-type two-phase flow regime at higher values of $\mathrm{Bo}$. Our numerical results are found to be in good agreement with recent experimental and theoretical works.

The nature of human-human interaction, specifically, how people synchronize with each other in multiple-participant conversations, is described by a ferromagnetic interaction model of people’s activity levels. We found two microscopic human interaction characteristics from a real-environment face-to-face conversation. The first characteristic is that people quite regularly synchronize their activity level with that of the other participants in a conversation. The second characteristic is that the degree of synchronization increases as the number of participants increases. Based on these microscopic ferromagnetic characteristics, a “conversation activity level” was modeled according to the Ising model. The results of a simulation of activity level based on this model well reproduce macroscopic experimental measurements of activity level. This model will give a new insight into how people interact with each other in a conversation.

The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. This article expands on our previously published work concerning a real-world billiard. Here we provide a detailed mathematical model for describing the motion of a realistic billiard for arbitrary boundaries, where we include rotational effects and additional forms of energy dissipation. Simulations of the model are applied to parabolic, wedge, and hyperbolic billiards that are driven sinusoidally. The simulations demonstrate that the parabola has stable, periodic motion, while the wedge and hyperbola (at high driving frequencies) appear chaotic. The hyperbola, at low driving frequencies, behaves similarly to the parabola, i.e., has regular motion. Direct comparisons are made between the model's predictions and previously published experimental data. The representation of the coefficient of restitution employed in the model resulted in approximate agreement with the experimental data for all boundary shapes investigated. We show how the coefficient of restitution varies under different model assumptions. It is shown that the data can be successfully modeled with a simple set of parameters.

We analyze weighted networks as randomly reinforced urn processes, in which the edge-total weights are determined by a reinforcement mechanism. We develop a statistical test and a procedure based on it to study the evolution of networks over time, detecting the “dominance” of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not. Distance from the steady state can be considered as a measure of the relevance of the observed properties of the network. Our results are quite general, in the sense that they are not based on a particular probability distribution or functional form of the random weights. Moreover, the proposed tool can be applied also to dense networks, which have received little attention by the network community so far, since they are often problematic. We apply our procedure in the context of the International Trade Network, determining a core of “dominant edges.”