We show that the decay of strongly excited oscillons in a single vacuum model reveals a chaotic, fractal-like pattern very much like the one found in kink-antikink collisions in the ${\varphi }^4$ model. This structure can be attributed to the resonant energy transfer mechanism triggered by the modulations of amplitudes of constituent oscillons which form the excited oscillon. We also find evidence that such modulations arise as a motion of two quasibreathers inside the constituent oscillon.

We extend the study of the inertial effects on the two-dimensional dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational dynamics to the translational one, produces unexpected and nontrivial dynamics, already at the deterministic level. Examining first the motion of a free particle, we contrast the role of inertia depending on the sign of the self-aligning torque. When positive, inertia does not alter the steady-state linear motion of an a-chiral self-propelled particle. On the contrary, for a negative self-aligning torque, inertia leads to the destabilization of the linear motion into a spontaneously broken chiral symmetry orbiting dynamics. Adding an active torque, or bias, to the angular dynamics, the bifurcation becomes imperfect in favor of the chiral orientation selected by the bias. In the case of a positive self-alignment, the interplay of the active torque and inertia leads to the emergence, out of a saddle-node bifurcation, of solutions which coexist with the simply biased linear motion. In the context of a free particle, the rotational inertia leaves unchanged the families of steady-state solutions but sets their stability properties. The situation is radically different when considering the case of a collision with a wall, where a very singular oscillating dynamics takes place which can only be captured if both translational and rotational inertia are present.

We study the orientational ordering properties of some quasi-one-dimensional hard-body fluids, where the anisotropic particles are confined to a straight line, while they are free to rotate in a plane. We examine a class of models where the close-packing structure is degenerate, i.e., the highest possible density can be realized with different orientational ordering. We find that the close-packing degeneracy always gives rise to a diverging orientational correlation, which can be a marker of phase transition, glass formation, and jamming. In the case of isotropic or partially ordered phases at the close-packing density, the diverging orientational correlation indicates a tendency for being a strongly ordered nematic phase. However, the orientational divergence in the perfect nematic phase shows that the particles must rotate in concert to go from one closely packed structure to another.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar mixing, e.g., inside a large-scale coherent vortex forming in two-dimensional turbulence or in elastic turbulence in a microchannel. We examine both the decaying case and the case of the continuous forcing of the scalar variances. In both cases dynamics possesses strong intermittency, which can be characterized via the single-point moments and correlation functions calculated in our work. We present general qualitative properties of pair correlation function as well as certain quantitative results obtained in the framework of the model with fluctuations that are short correlated in time.

Improvement in the functionality of an inertial electrostatic confinement fusion (IECF) device has been investigated through kinetic simulation. Previously, we achieved a neutron generation rate of ${10}^6$ neutrons per second, but higher rates and better plasma confinement are necessary for broader applications. We compared a traditional single-grid IECF device with a triple-grid variant to evaluate the benefits of using multiple grids for ion confinement. Our computational models, using the 2D-3V xoopic code, suggest that the triple-grid device, with its optimized potentials, could significantly enhance ion confinement. The models show that the triple-grid design directs ion beams more effectively to the center, in contrast with the more scattered ion distribution in the single-grid design. This results in longer ion lifetimes in the triple-grid system due to its modified electrostatic fields. In the standard single-grid IECF device, the primary reasons for ion loss are chaotic ion trajectories and interactions with residual gases. By operating the triple-grid device under very low background gas pressure and with a focused field structure, we expect to achieve improved ion confinement.

We use a recently developed a kinetic model derived from the Dirac equation to study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The leading contribution to the conductivity tensor in such a plasma is calculated. It is found that the electron Hall current has an anomalous contribution, in the quantum relativistic regime, where the effective particle energy has a significant contribution from the diamagnetic and Zeeman energy. As a result, a new quantum resonance frequency appears, and the dispersion relation for the left- and right-hand polarized modes are strongly modified for long and moderate wavelengths. The implications for magnetar physics are discussed.

We investigate parametric decay instability (PDI) of circularly polarized Alfvén wave into daughter acoustic wave and backward Alfvén wave in magnetically dominated plasma, in which the magnetization parameter $\sigma$ (energy density ratio of background magnetic field to matter) exceeds unity. We analyze relativistic magnetohydrodynamics (MHD), focusing on wave frequencies sufficiently lower than the plasma and cyclotron frequencies. We derive analytical formulas for the dispersion relation and growth rate of the instability as a function of the magnetization $\sigma$, wave amplitude $\eta$, and plasma temperature $\theta$. We find that PDI persists even in high magnetization $\sigma$, albeit with a decreased growth rate up to $\sigma \to \infty$. Our formulas are useful for estimating the decay of Alfvén wave into acoustic wave and heat in high magnetization $\sigma$ plasma, which is a ubiquitous phenomenon such as in pulsars, magnetars, and fast radio bursts.

We present a comprehensive analysis of the non-Newtonian lattice Boltzmann method (LBM) when it is used to simulate the distribution of wall shear stress (WSS). We systematically identify sources of numerical errors associated with non-Newtonian rheological behavior of fluids in off-grid geometries. We implement the single relaxation time, Bhatnagar-Gross-Krook (BGK), and multiple relaxation time (MRT) collision operators and investigate flow in a two-dimensional channel aligned with lattice directions and off-grid Hagen-Poiseuille flow of Ostwald–de Waele (power-law) fluids. As for boundary conditions, we implement constant body force-driven and pressure-driven flows. These two boundary conditions have different numerical challenges, which include numerical stability, accuracy, mass conservation, and compressibility effects, which are inherent in the LBM method. Our results indicate that MRT, when the relaxation times are adequately tuned in the non-Newtonian case, significantly improves the WSS distribution accuracy and the numerical stability of the LBM. MRT also enhances the stability and accuracy for non-Newtonian fluids compared with the Newtonian case, meaning that it is questionable if a BGK collision operator is appropriate to use in a non-Newtonian case with off-grid boundaries. When analyzing the non-Newtonian LBM in the context of staircase walls and interpolated bounce-back (IBB) walls, a MRT collision operator with the appropriate choice of tunable relaxation times makes it possible to achieve numerically accurate results without a significant increase in grid resolution for matching to the analytical solution of WSS distributions.

In analyzing the non-Newtonian flows, we show that the viscosity dependency of bounce-back walls in the BGK-LBM deviates from the results obtained under Newtonian assumptions. The power-law index further influences these discrepancies, and errors caused by the viscosity dependency of the bounce-back boundary conditions can be effectively mitigated by implementing the MRT procedure. Results show that non-Newtonian fluids, in contrast with the Newtonian assumption, encounter a greater mass imbalance when flowing through a periodic system with IBB walls. MRT can address this challenge, as it allows for independent adjustments of physical relaxation times and enhances mass conservation in the case of non-Newtonian fluids. In pressure-driven non-Newtonian flows, there is a significant impact of bulk viscosity. This aspect is often overlooked in Newtonian simulations but can significantly impact fluid adapting to rapid changes in local effective viscosity. One of our main conclusions is that the MRT collision operator with tuned relaxation times can effectively resolve numerical problems caused by non-Newtonian rheological properties and off-grid geometries. We also provide practical guidelines for selecting the most suitable simulation approach.

Asymptotic freedom is a feature of quantum chromodynamics that guarantees its well posedness. We derive an analog of asymptotic freedom enabling unconditional linear stability of lattice Boltzmann simulation of hydrodynamics. We further demonstrate the validity of the derived conditions via the special case of the equilibrium based on entropy maximization, which is shown to be uniquely renormalizable.

Temporal environmental noise (EN) is a prevalent natural phenomenon that controls population and community dynamics, shaping the destiny of biological species and genetic types. Conventional theoretical models often depict EN as a Markovian process with an exponential distribution of correlation times, resulting in two distinct qualitative dynamical categories: quenched (long environmental timescales) and annealed (short environmental timescales). However, numerous empirical studies demonstrate a fat-tailed decay of correlation times. Here we study the consequences of power-law correlated EN on the dynamics of isolated and competing populations. We analyze the intermediate region that lies between the quenched and annealed regimes and show that it can widen indefinitely. Within this region, dynamics is primarily driven by rare, yet not exceedingly rare, long periods of almost-steady environmental conditions. For an isolated population, the time to extinction in this region exhibits a power-law scaling with the logarithm of the abundance and also a nonmonotonic dependence on the spectral exponent.

The predicted implosion performance of deuterium-tritium fuel capsules in indirect-drive inertial confinement fusion experiments relies on precise calculations of the x-ray drive in laser-heated cavities (hohlraums). This requires accurate, spectrally dependent simulations of laser to x-ray conversion efficiencies and x-ray absorption losses to the hohlraum wall. A set of National Ignition Facility experiments have identified a cause for the long-standing hohlraum “drive deficit” as the overprediction of gold emission at ∼2.5 keV in nonlocal thermodynamic equilibrium coronal plasma regions within the hohlraum. Reducing the emission and absorption opacity in this spectral region by ∼20% brings simulations into agreement with measured x-ray fluxes and spectra.

Nuclear reactor cores achieve sustained fission chain reactions through the so-called “critical state”—a subtle equilibrium between their material properties and their geometries. Observed at macroscopic scales during operations, the resulting stationary neutron field is tainted by a noise term that hinders various fluctuations occurring at smaller scales. These fluctuations are either of a stochastic nature (whenever the core is operated at low power) or related to various perturbations and vibrations within the core, even operated in its power regime. For reasons that are only partially understood using linear noise theory, incidental events have been reported, characterized by an increase of the power noise. Such events of power noise growth, sometimes up to seemingly unbounded levels, have already led in the past to voluntary scramming of reactors. In this paper, we will use a statistical field theory of critical processes to model the effects of neutron power noise. We will show that the evolution of the neutron field in a reactor is intimately connected to the dynamic of surface growths given by the Kardar-Parisi-Zhang equation. Recent numerical results emerging from renormalization-group approaches will be used to calculate a threshold in the amplitude of the reactor noise above which the core enters a new criticality state, and to estimate the critical exponents characterizing this phase transition to rough neutron fields. The theoretical model of nonlinear noise built in this paper from ab initio statistical mechanics principles will be correlated and compared to data of misunderstood reactor noise levels and reactor instabilities and will be shown to provide both qualitative and quantitative insights into this long-standing issue of reactor physics.

We demonstrate the unique capabilities of the Wigner function, particularly in its positive and negative parts, for exploring the phase diagram of the spin $\text{−}\left(\frac{1}{2}\text{−}\frac{1}{2}\right)$ and $\text{spin}\text{−}\left(\frac{1}{2}\text{−}1\right)$ Ising-Heisenberg chains. We highlight the advantages and limitations of the phase-space approach in comparison with the entanglement concurrence in detecting phase boundaries. We establish that the equal angle slice approximation in the phase space is an effective method for capturing the essential features of the phase diagram but falls short in accurately assessing the negativity of the Wigner function for the homogeneous $\text{spin}\text{−}\left(\frac{1}{2}\text{−}\frac{1}{2}\right)$ Ising-Heisenberg chain. In contrast, we find for the inhomogeneous $\text{spin}\text{−}\left(\frac{1}{2}\text{−}1\right)$ chain that an integral over the entire phase space is necessary to accurately capture the phase diagram of the system. This distinction underscores the sensitivity of phase-space methods to the homogeneity of the quantum system under consideration.

We describe a generalized algorithm for evaluating the steady-state solution of the density matrix equation of motion, for the pump-probe scheme, when two fields oscillating at different frequencies couple the same set of atomic transitions involving an arbitrary number of energy levels, to an arbitrary order of the harmonics of the pump-probe frequency difference. We developed a numerical approach and a symbolic approach for this algorithm. We have verified that both approaches yield the same result for all cases studied, but require different computation time. The results are further validated by comparing them with the analytical solution of a two-level system to first order. We have also used both models to produce results up to the third order in the pump-probe frequency difference, for two-level systems, and up to first order for three- and four-level systems. In addition, we have used this model to determine accurately, the gain profile for a self-pumped Raman laser, for a system involving 16 Zeeman sublevels in the D1 manifold of ${}^{87}\mathrm{Rb}$ atoms. We have also used this model to determine the behavior of a single-pumped superluminal laser. In many situations involving the applications of multiple laser fields to atoms with many energy levels, one often makes the approximation that each field couples only one transition, because of the difficulty encountered in accounting for the effect of another field coupling the same transition but with a large detuning. The use of the algorithm presented here would eliminate the need for making such approximations, thus improving the accuracy of numerical calculations for such schemes.

We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice and the more tractable mean-field model corresponding to infinite-ranged coupling between all sites. In the high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be written as a series in half odd integer powers of the inverse temperature, $k$, with the leading term $\sim k^{1/2}$. This result is true in any dimension and for arbitrary lattices. We also show that the coefficients of the expansion satisfy simple identities (akin to sum rules) for the nearest-neighbor case. These identities are verified numerically by computing the exact partition function for a two-dimensional square lattice of size $16\times 16$. For the mean-field model, we write down the partition function (termed the mean-field polynomials) for the ferromagnetic (FM) and antiferromagnetic (AFM) cases and derive from them the mean-field equations. We analytically show that at high temperatures the zeros of the AFM mean-field polynomial scale as $\sim k^{1/2}$ as well. Using a simple numerical method, we find the roots lie on certain curves (the root curves), in the thermodynamic limit for the mean-field polynomials for the AFM case as well as for the FM one. Our results show a new root curve that was not found earlier. Our results also clearly illustrate the phase transition expected for the FM and AFM cases, in the language of Yang-Lee zeros. Moreover, for the AFM case, we observe that the root curves separate two distinct phases of zero and nonzero complex staggered magnetization, and thus depict a complex phase boundary.

In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum observables, which we refer to as a thermodynamic uncertainty relation (TUR) for the entropy production. In the absence of coherence between the states, our result reproduces classic TURs in stochastic thermodynamics. For the derivation of the TUR, we introduce a lower bound for a quantum generalization of the ${\chi }^2$ divergence between two states and discuss its implications for stochastic and quantum thermodynamics, as well as the limiting case where it reproduces the quantum Cramér-Rao inequality.

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a growing interest in the development of analogous approaches for DDEs to understand their response to external forcing. When combined with Floquet theory, the fundamental quantities for this reduction are phase and amplitude response functions. Here, we develop a framework for their construction that utilizes the method of harmonic balance.