The outflow velocity of expanding deuterium-tritium (DT) fuel can become significant after the bangtime, approaching local ion thermal velocity when the inertial confinement fusion (ICF) hotspot surpasses the ignition threshold. Under such conditions, the conventional assumption of an isotropic target-particle velocity distribution becomes questionable and the influence of bulk fluid motion on alpha-particle transport should be examined. In this paper we derive an analytical expression of the charged-particle stopping power in plasmas with arbitrary bulk fluid motion. We then apply this formalism to alpha-particle transport in an ICF hotspot. The results suggest that incorporating the background fluid velocity into the alpha-particle transport simulation results in a greater fraction of alpha-particle energy being transferred directly to the D and T ions, with a corresponding decrease in the energy deposited to electrons. These results indicate a potentially important correction to alpha-energy deposition in the post-bangtime hotspot.
Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other points of interest (POIs) across cities. However, the mechanisms by which such heavy-tailed behaviors emerge from local urban dynamics remain poorly understood. In this work we demonstrate that global inhomogeneity in the spatial distribution of POIs can arise from the aggregation of locally homogeneous processes. Using Foursquare data from the city of Bologna, we show that POI distributions exhibit clear power-law scaling when analyzed at city scale. We develop a theoretical framework in which this behavior naturally emerges from spatial clusters defined by shared intensity levels across disjoint areas, rather than spatial contiguity. By analytically and empirically linking these local processes to the observed global distribution, we provide a generative explanation for the emergence of scale-free patterns in urban commercial structure. To further relax the assumptions underlying the purely spatial model, and to account for the empirical observation that areas with similar activity intensity can be spatially disjoint, we introduce a hybrid hierarchical approach that combines spatial clustering with statistical heterogeneity across regions of comparable density, modeled via Poisson mixtures. This enables us to capture real-world deviations from local regularity while preserving interpretability. Our findings highlight a key insight: complex global phenomena in cities can arise from the spatial superposition of simple, locally uniform dynamics. This connection between microlevel homogeneity and macroscale complexity offers tools for interpreting, modeling, and classifying urban space.
We study the 6 model and derive two broad classes of lattice discretizations that admit static, translationally invariant kinks; that is, stationary kink profiles that can be centered at an arbitrary position relative to the lattice. These discretizations are constructed using a one-dimensional map, n+1 = F( n), which provides a direct and systematic algorithm for generating such models. Numerical computations for two representative cases show that the discrete kinks do not possess internal modes, consistent with the continuum theory, although an additional high-frequency mode may appear above the upper edge of the phonon band. We also show that generic discretizations of the 6 model do not support static kink solutions. Instead, the resulting dynamics produce autotraveling and self-accelerating kinks that propagate at the maximal group velocity while continuously emitting radiation.
Nonequilibrium steady states are investigated in a two-dimensional billiard table, called the Lorentz circuit, consisting of two circular urns connected by two rectangular strips: an active channel, where a feedback mechanism operates, and a passive finite-size Lorentz channel, which is a finite network of Sinai billiards, i.e., a specific environment populated with an array of circular scatterers of fixed radius. We show that, in the finite-horizon regime, a variation of any of the four geometrical parameters of the Lorentz channel can trigger a phase transition in the circuit. Our analytic derivations identify the critical parameters governing these transitions and predict whether they are continuous or discontinuous. We find that both transition orders are realized upon changing just one of the geometrical parameters. Our analysis further highlights the validity of Fick's law in the Lorentz channel, which in our model mirrors the validity of Ohm's law in electrical circuits. All analytic results are corroborated by an extensive set of numerical simulations of the particle dynamics.
We investigate the critical phenomena of the asymmetric quantum Rabi model (AQRM), where parity symmetry is broken by an external bias. Through both analytical and numerical calculations, we identify second-order and first-order phase transitions, with the latter absent in the standard quantum Rabi model. We derive an analytical two-variable scaling function that describes the finite-frequency scaling behavior of the AQRM, and numerical results confirm this framework. The introduction of bias leads to additional critical exponents, including a bias-related critical exponent ν_{h} and susceptibility exponent γ. Moreover, we demonstrate that critical scaling persists even below the conventional critical coupling, indicating the emergence of field-induced quantum criticality. These findings establish a robust theoretical framework for understanding universal quantum criticality in light-matter systems.
