A very fast method for calculating line shapes in the presence of an external magnetic field accounting for charge particle dynamics is proposed. It is based on a reformulation of the frequency fluctuation model, which provides an expression of the dynamic line shape as a functional of the static distribution function of frequencies. In the presence of an external magnetic field, the distribution of intensity and polarization of the emission depends on the angle between the observation line and the magnetic field’s direction. Comparisons with numerical simulations and experimental results for various plasma conditions show very good agreement. Results on hydrogen lines in the context of magnetic fusion and the Lyman-$\alpha$ line, accounting for fine structure, emitted by argon in the context of inertial fusion, are also presented.

Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton’s laws extends them to relativistic motion.

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region ($J<0$). In the $J\to -\infty$ limit, we map the AT model onto a fully packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region $J<0$ and $K>0$, with $K$ the four-spin interaction. Further, we find that, in the $J\to -\infty$ limit, the critical line terminates at the decoupled point $K=0$. From the numerical results and the exact mapping, we conjecture that this “tricritical” point ($J\to -\infty ,K=0$) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as $z=0.28\left(1\right)$ near $(J\to -\infty ,K=0)$.

We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated.

We consider a one-dimensional Brownian motion under nonequilibrium feedback control. Generally, the fluctuation-dissipation theorem (FDT) is violated in driven systems under nonequilibrium conditions. We find that the degree of the FDT violation is bounded by the mutual information obtained by the feedback system when the feedback protocol includes measurement errors. We introduce two simple models to illustrate cooling processes by feedback control and demonstrate analytical results for the cooling limit in those systems. Especially in a steady state, lower bounds to the effective temperature are given by an inequality similar to the Carnot efficiency.

We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension $d⩾2$. Exploiting the nonuniqueness of the renormalization-group cutoff scheme, we find, however, that the capillary parameter $\omega$ is a scheme-dependent quantity below $d=3$. For $d=3$ the parameter $\omega$ is perfectly robust against scheme variation.

Tumor interstitial fluid pressure (TIFP) has the potential to predict tumor response to nonsurgical cancer treatments, including radiation therapy. At present the only quantitative measures available are of limited use, since they are invasive and yield only point measurements. We present the mathematical framework for a quantitative, noninvasive measure of TIFP. The model describes the distribution of interstitial fluid pressure in three distinct tumor regions: vascularized tumor rim, central tumor region, and normal tissue. A relationship between the TIFP and the fluid flow velocity at the periphery of a tumor is presented. This model suggests that a measure of fluid flow rate from a tumor into normal tissue reflects TIFP. We demonstrate that the acquisition of serial images of a tumor after the injection of a contrast agent can provide a noninvasive and potentially quantitative measure of TIFP.

In nonequilibrium states, currents are produced by irreversible processes that take a system toward the equilibrium state, where the current vanishes. We demonstrate, in a general setting, that superstatistics arises when the system relaxes to a (stationary) quasiequilibrium state instead, where only the mean current vanishes because of fluctuations. In particular, we show that a current with Gaussian white noise takes the system to a unique class of quasiequilibrium states, where the superstatistics coincides with Tsallis escort $q$ distributions. Considering the fully developed turbulence as an example of such quasiequilibrium states, we analytically deduce the power-law spectrum of the velocity structure functions, yielding a correction to the log-normal model, which removes its shortcomings with regard to the decreasing higher order moments and the Novikov inequality, and obtain exponents that agree well with the experimental data.

We study the spreading of information on technological developments in socioeconomic systems where the social contacts of agents are represented by a network of connections. In the model, agents get informed about the existence and advantages of new innovations through advertising activities of producers, which are then followed by an interagent information transfer. Computer simulations revealed that varying the strength of external driving and of interagent coupling, furthermore, the topology of social contacts, the model presents a complex behavior with interesting novel features: On the macrolevel the system exhibits logistic behavior typical for the diffusion of innovations. The time evolution can be described analytically by an integral equation that captures the nucleation and growth of clusters of informed agents. On the microlevel, small clusters are found to be compact with a crossover to fractal structures with increasing size. The distribution of cluster sizes has a power-law behavior with a crossover to a higher exponent when long-range social contacts are present in the system. Based on computer simulations we construct an approximate phase diagram of the model on a regular square lattice of agents.

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the interarrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM reaching a single user. We study the behavior of the message interarrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying interarrival times at any node of the network.

Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^{\gamma }(\gamma =1)$. However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship $T\propto P^{\gamma }(\gamma >1)$ is in fact ubiquitous in online activities such as microblogging, news voting, and photo tagging. We call the pattern “accelerating growth” and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate $\gamma$ associates with a scaling parameter $b$ in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is worth further exploration.

Chaotic transport in a Hamiltonian system perturbed by a weak turbulent wave field is studied. It is assumed that a turbulent wave field has a wide spectrum containing up to thousands of modes whose phases are fluctuating in time with a finite correlation time. To integrate the Hamiltonian equations a fast symplectic mapping is derived. It has a large time-step equal to one full turn in angle variable. It is found that the chaotic transport across tori caused by the interactions of small-scale resonances have a fractal-like structure with the reduced or zero values of diffusion coefficients near low-order rational tori thereby forming transport barriers there. The density of rational tori is numerically calculated and its properties are investigated. It is shown that the transport barriers are formed in the gaps of the density of rational tori near the low-order rational tori. The dependencies of the depth and width of transport barriers on the wave field spectrum and the correlation time of fluctuating turbulent field (or the Kubo number) are studied. These numerical findings may have importance in understanding the mechanisms of transport barrier formation in fusion plasmas.

A term-ranking approach is proposed to globally model the underlying dynamics of a chaotic series. The basic idea of this approach is to rank candidate bases before they are used to construct the global model. The ranked bases are involved in the global model one by one in a sequence from high to low until the best model is found. Simulations show that the model obtained by the term-ranking approach has a much longer prediction time, but fewer coefficients, than the widely used standard model. The proposed approach is also successfully applied to coding and synthesis of chaoslike voice data, showing promise for its use with truly noisy experimental data.

An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of material particles and is to linearly regress to the equilibrium. We propose a local functional which is expected to represent the total entropy of the larger system and require the entropy functional to be maximized in the process of linear regression. We show that Onsager’s original idea on linear regression can then be realized explicitly as current conservations with dissipative currents in the desired form. We demonstrate the effectiveness of this formulation by showing that one can treat a wide class of relativistic continuum materials, including standard relativistic viscous fluids and relativistic viscoelastic materials.

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager’s linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

When a high voltage is applied to a liquid pumped through a needle, charged microdroplets can be formed, which are carried along the electric field lines. This phenomenon is called electrohydrodynamic atomization (EHDA), or simply electrospray. In this work we show that in the case of water, droplets may reverse their paths flying back toward the liquid meniscus, sometimes making contact with it. Such reverse movement is caused by polarization of the water inside the strong electric field. To understand this phenomenon we developed a way to calculate the droplet charge using its trajectory obtained by high-speed imaging. The values found showed that these droplets are charged between 2.5% and 19% of their Rayleigh limit.

High-precision numerical simulations of vortex sheets in two-dimensional flows show a cascade of Kelvin-Helmholtz instabilities and the appearance of a large spectrum of spatial scales. We found a physical mechanism, combining advection and self-interaction of the sheet vorticity, that leads to the formation of a flow singularity. An unexpected consequence of these singularities and of the complex vorticity distribution along the sheet is the emergence of an energy spectrum following a power law.

In this paper, we consider a concentration grating of magnetic nanoparticles optically induced by thermodiffusion in a layer of ferrofluid in the presence of the external homogeneous magnetic field. The applied field is directed along the concentration gradient and leads to the appearance of the internal nonhomogeneous demagnetizing fields. When the system reaches equilibrium, the optical pumping is switched off, and the grating is allowed to relax. We carry out a stability analysis using the Galerkin approach and numerical simulations of the full system of equations to determine the growth rates and the mode amplitudes of the hydrodynamic and concentration perturbations during the relaxation stage.

In this paper, we develop the analysis of a two-dimensional magnetohydrodynamical configuration for an axially symmetric and rotating plasma (embedded in a dipolelike magnetic field), modeling the structure of a thin accretion disk around a compact astrophysical object. Our study investigates the global profile of the disk plasma, in order to fix the conditions for the existence of a crystalline morphology and ring sequence, as outlined by the local analysis pursued in Coppi [Phys. Plasmas 12, 7302 (2005)] and Coppi and Rousseau [Astrophys. J. 641, 458 (2006)]. In the linear regime, when the electromagnetic back-reaction of the plasma is small enough, we show the existence of an oscillating radial behavior for the flux surface function, which very closely resembles the one outlined in the local model, apart from a radial modulation of the amplitude. In the opposite limit, corresponding to a dominant back-reaction in the magnetic structure over the field of central object, we can recognize the existence of a ringlike decomposition of the disk, according to the same modulation of the magnetic flux surface, and a smoother radial decay of the disk density, with respect to the linear case. In this extreme nonlinear regime, the global model seems to predict a configuration very close to that of the local analysis, but here the thermostatic pressure, crucial for the equilibrium setting, is also radially modulated. Among the conditions requested for the validity of such a global model, the confinement of the radial coordinate within a given value sensitive to the disk temperature and to the mass of the central objet, stands; however, this condition corresponds to dealing with a thin disk configuration.

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper, we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that, by using the extended Dirac bracket definition, it will be possible to analyze more deeply gauge theories starting with second-class systems.