Search Results (41)

We advance a mathematical framework for collective conviction by deriving a continuum theory from the network-based model introduced by us recently. The resulting equation governs the evolution of belief through a degenerate anisotropic logistic–diffusion process, where diffusion slows as conviction saturates. In one spatial dimension, we prove global well-posedness, demonstrate spectral front pinning that arrests the spread of influence at finite depth, and construct explicit traveling-wave solutions. In two dimensions, we uncover a geometric mechanism of curvature–induced quenching, where belief propagation halts along regions of low effective mobility and curvature. Building on this insight, we formulate a variational principle for optimal control under resource constraints. The derived feedback law prescribes how to spatially allocate repression effort to maximize inhibition of front motion, concentrating resources along high-curvature, low-mobility arcs. Numerical simulations validate the theory, illustrating how localized suppression dramatically reduces transverse spread without affecting fast axes. These results bridge analytical modeling with societal phenomena such as protest diffusion, misinformation spread, and institutional resistance, offering a principled foundation for selective intervention policies in structured populations. Full article

Pressure relief devices are critical for the safe release of pressurized hydrogen. To address the risk of spontaneous ignition during a high-pressure release, three-dimensional (3D) numerical simulations are systematically conducted to investigate the effects of burst conditions on spontaneous ignition behavior. Eight simulation cases are considered, involving two opening processes (instantaneous and 10-step-like), three burst disk shapes (flat, conventional domed, and reverse domed), and five opening ratios (1, 0.8, 0.6, 0.4, and 0.2). The 10-step-like opening enhances jet turbulence and promotes flame merging between the boundary layer and jet front, intensifying combustion. Domed structures cause a high-velocity region behind the leading shock wave, altering jet front evolution. Compared with reverse-domed disks, flat and conventional domed disks generate stronger vortices and a larger shock-heated area, resulting in more severe combustion and elevated fire risk. As the opening ratio decreases, both shock wave strength and propagation velocity drop significantly, and spontaneous ignition does not occur. The opening ratio has minimal influence on the distance traveled by shock-induced heating. These findings offer meaningful guidance for the design and manufacture of pressure relief devices for the safe emergency release of hydrogen. Full article

The Carpathian orogen represents a natural laboratory for the study of geodynamic interactions between lithospheres of different ages. The ancient Archean Cratons, such as the East European Craton, and Proterozoic platforms like the Scythian and Moesian platforms collided with the younger Tisza and Dacia mega-units, resulting in the formation of the current architecture of the Carpathian Mountains. To better understand how the lithospheric structure on Romanian territory changes from the East European Craton to younger European microplates, we use earthquake data recorded at the permanent broadband seismic stations of the Romanian National Seismic Network (RSN). Applying the multiple filter technique, we examine the dispersion of Rayleigh wave group velocities for earthquakes located within a 4000 km radius of the epicenter. Travel time tomography, conducted through fast marching surface tomography, helps us to construct group velocity maps for periods between 30 and 80 s. Our findings highlight a low-velocity body in front of the Vrancea slab, indicating asthenospheric upwelling due to slab verticalization. Full article

In an autonomous robotic space debris removal mission, an essential sensor used for navigation is an FMCW radar designed for close-range relative navigation. To achieve the required range performance, minimizing RF leakage between the transmitter (Tx) and receiver (Rx) antennas is essential for the accurate detection of the range and velocity of the targeted space debris. Antennas positioned above the metallic satellite front face are highly susceptible to RF leakage, primarily caused by surface current propagation and lateral waves traveling parallel to the platform. This study presents two lightweight, single-layer planar metamaterials—a novel compact electromagnetic bandgap (EBG) and a non-uniform high-impedance surface (HIS)—optimized to suppress both surface waves and interact with space waves within the 9.3–9.8 GHz frequency range. These designs address strict size, weight, and power (SWaP) constraints while ensuring compatibility with extreme space conditions and resistance to mechanical shocks. Experimental validation indicates that a minimum Tx/Rx isolation improvement of 10 dB is achieved using the HIS, and 20 dB is achieved using the EBG across the radar’s operational bandwidth (5%). Full article

In this study, we used the Sanya Incoherent Scatter Radar (SYISR) to observe the altitude profiles of traveling ionospheric disturbances (TIDs) during a moderate magnetic storm from 13 to 15 March 2022. Three TIDs were recorded, including two large-scale TIDs (LSTIDs) and one medium-scale TID (MSTID). These LSTIDs occurred during the storm recovery phase, characterized by periods of ~110–155 min, downward phase velocities of 22–60 m/s, and a relative amplitude of 17–25%. A nearly vertical front was noted at ~350–550 km, differing from AGW theory predictions. This structure is more attributed to the combined effects of sunrise-induced electron density changes and pre-sunrise uplift. Moreover, GNSS observations linked this LSTID to high-latitude origins, indicating a connection to polar magnetic storm excitation. However, the second LSTID was observed at lower altitudes (150–360 km) with a higher elevation angle (~17°). This LSTID, observed by the SYISR, was absent in the GNSS data from mainland China and Japan, suggesting a potential local source. The MSTID exhibited a larger relative amplitude of 29–36% at lower altitudes (130–210 km) with severe upward attenuation. The MSTID may be related to atmospheric gravity waves from the lower atmosphere. AGWs are considered to be the perturbation source for this MSTID event. Full article

Mainline coordinated control is usually based on fixed speed and statistical traffic flow by period. However, in actual operation, the vehicles parked in front of the intersection and the arriving vehicles often fluctuate, and the through-traffic green time is wasted due to phase transition, which leads to mismatches between the signal plans and actual traffic flow requirements, affecting the traffic efficiency of the intersection. To address the above issues, using vehicle–road collaborative control (VRCC), by calculating the phase difference lead time and phase difference of adjacent intersections, the green extension time for the green wave through-traffic phase, and the guiding vehicle speed, the goal of reducing the detention volume of through traffic, reducing the waste of through-traffic green time caused by phase transitions and improving the throughput of through traffic can be achieved. The speed of the green wave traffic flow is increased by guiding vehicles to form saturated platoons during green periods. Finally, PTV VISSIM 4.3 was used for simulation verification, and the results showed that compared to not implementing the control strategy, the average delay on the arterial road was reduced by 85.1%, the average number of stops was reduced by 84.3%, the average travel time was reduced by 34%, and the average queue length was reduced by 62.6%. This significantly improved the efficiency of traffic on the arterial road and effectively reduced congestion. Full article

Two (consecutive) reductions of the complete Gatenby–Gawlinski model for cancer invasion are proposed in order to investigate the mathematical framework, mainly from a computational perspective. After a brief overview of the full model, we proceed by examining the case of a two-equations-based and one-equation-based reduction, both obtained by means of a quasi-steady-state assumption. We focus on invasion fronts, exploiting a numerical strategy based on a finite volume approximation, and perform corresponding computational simulations to study the sharpness/smoothness of the traveling waves. Then, we employ a space-averaged wave speed estimate—referred to as the LeVeque–Yee formula—to quantitatively approach the propagation phenomenon. Concerning the one-equation-based model, we propose a scalar degenerate reaction-diffusion equation, which proves to be effective in order to qualitatively recover the typical trends arising from the Gatenby–Gawlinski model. Finally, we carry out some numerical tests in a specific case where the analytical solution is available. Full article

To provide insights into the spreading speed and propagation dynamics of viruses within a host, in this paper, we investigate the traveling wave solutions and minimal wave speed for a degenerate viral infection dynamical model with a nonlocal dispersal operator and saturated incidence rate. It is found that the minimal wave speed $c^{\ast }$ is the threshold that determines the existence of traveling wave solutions. The existence of traveling fronts connecting a virus-free steady state and a positive steady state with wave speed $c\ge c^{\ast }$ is established by using Schauder’s fixed-point theorem, limiting arguments, and the Lyapunov functional. The nonexistence of traveling fronts for $c<c^{\ast }$ is proven by the Laplace transform. In particular, the lower-bound estimation of the traveling wave solutions is provided by adopting a rescaling method and the comparison principle, which is a crucial prerequisite for demonstrating that the traveling semifronts connect to the positive steady state at positive infinity by using the Lyapunov method and is a challenge for some nonlocal models. Moreover, simulations show that the asymptotic spreading speed may be larger than the minimal wave speed and the spread of the virus may be postponed if the diffusion ability or diffusion radius decreases. The spreading speed may be underestimated or overestimated if local dispersal is adopted. Full article

The propagation of detonation waves (i.e., supersonic combustion waves) in non-uniform gaseous mixtures has become a matter of interest over the past several years due to the development of rotating detonation engines. It was shown in a number of recent theoretical studies of one-dimensional pulsating detonation that perturbation of the parameters in front of the detonation wave can lead to a resonant amplification of intrinsic pulsations for a certain range of perturbation wavelengths. This work is dedicated to the clarification of the mechanism of this effect. One-dimensional reactive Euler equations with single-step Arrhenius kinetics were solved. Detonation propagation in a gas with sine waves in density was simulated in a shock-attached frame of reference. We carried out a series of simulations, varying the wavelength of the disturbances. We obtained a non-linear dependence of the amplitude of these pulsations on the wavelength of disturbances with resonant amplification for a certain range of wavelengths. The gain in velocity was about 25% of the Chapman–Jouguet velocity of the stable detonation wave. The effect is explained using the characteristic analysis in the x-t diagram. For the resonant case, we correlated the pulsation period with the time it takes for the C₊ and C₋ characteristics to travel through the effective reaction zone. A similar pulsation mechanism is realized when a detonation wave propagates in a homogeneous medium. Full article

Using linear elasticity theory, we describe the mechanical response of dry non-cohesive granular masses of Ottawa sand contained by spherical rubber balloons subject to sudden bursting in the earliest instants of the event. Due to the compression imposed by the balloon, the rupture produces a fast radial expansion of the sand front that depends on the initial radius $R_0$, the initial pressure p originated by the balloon, and the effective modulus of compression $K_e$. The hydrostatic compression approximation allows for the theoretical study of this problem. We found a linear decompression wave that travels into the sand and that induces a radial expansion of the granular front in the opposite direction with similar behavior to the wave but with a slightly lower speed. Full article

We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. To simulate the model in two-dimensional space, we use the continuous Runge–Kutta method of the fourth order and the discrete Runge–Kutta method of the third order with six stages. The numerical results admit the existence of traveling wave solutions for the proposed model. We use the COVID-19 epidemic to conduct numerical experiments and investigate the minimal speed of spread of the traveling wave front. The minimal spreading speeds of COVID-19 are found and discussed. Also, we assess the power of containment measures to contain the epidemic. The results depict a clear drop in the spreading speed of the traveling wave front after applying containment measures to at-risk populations. Full article

We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some initial positions chaos occurs and for others it does not. In a space-homogeneous system, we need at least three fronts to create time-periodic behaviour, while to create chaos, we should have four fronts. We also provide a short review of previously known results, and different known mechanisms of chaos generation for reaction–diffusion systems. Our results can be used for pattern coding, in particular, for morphogenesis. Full article

The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology. Full article

In this work, we find analytical solutions to the Chavy-Waddy–Kolokolnikov equation, a continuum approximation for modeling aggregate formation in bacteria moving toward the light, also known as phototaxis. We used three methods to obtain the solutions, the generalized Kudryashov method, the $e^{-R\left(\xi \right)}$-expansion, and exponential function methods, all of them being very efficient for finding traveling wave-like solutions. Findings can be classified into the case where the nonlinear term can be considered a small perturbation of the linear case and the regime of instability and pattern formation. Standing waves and traveling fronts were also found among the physically interesting cases, in addition to recovering stationary spike-like solutions. Full article

In this article, a Ka-band broadband analog predistortion (APD) microwave monolithic integrated circuit (MMIC) with independent tunability based on a 0.15 μm GaAs pHEMT process is proposed, which can be cascaded in front of traveling wave tube amplifiers (TWTAs) to improve their linearity. The influence of different diode sizes on the parameters of Schottky diodes is analyzed and used to design the gain and phase nonlinear branches. The broadband APD MMIC is realized based on a dual-branch vector synthesis design and nonlinear frequency adjust module (NFAM). The independent tunability and broadband characteristics of the APD MMIC are verified by simulated and measured results with an error of less than 5%. Furthermore, a Ka-band 60 W TWTA is linearized by the APD MMIC, and the gain and phase compressions are reduced from 8 dB and 50° to within 3 dB and 12°, respectively. The third-order intermodulation (C/IM3) is greater than 28 dBc and noise power ratio (NPR) is greater than 15.7 dBc at 3 dB output power backoff (OPBO) over the operating band of 25.1~27.5 GHz, indicating that the APD MMIC can improve the nonlinearity of TWTA effectively under broadband signals. Full article