Class Of Solutions Research Articles

Global classical solutions for three-dimensional compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in bounded domains

In this paper, we study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier–Stokes equations with Coulomb force [S. Liu, X. Xu and J. Zhang, Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier–Stokes–Poisson equations subject to large oscillations and non-flat doping profile, J. Differ. Equ. 269 (2020) 8468–8508] and compressible MHD equations [H. Li, X. Xu and J. Zhang, Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum, SIAM J. Math. Anal. 45 (2013) 1356–1387] to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity.

Nonlinear transmission exponent for boundedness of solutions to a chemotaxis system with indirect signal production

This paper deals with the Neumann initial–boundary problem for a fully parabolic chemotaxis system with indirect signal production, and the size of phenotypic transmission exponent is identified to guarantee the global existence and boundedness of classical solutions to the problem with suitably regular initial data.

PC-ILP: A Fast and Intuitive Method to Place Electric Vehicle Charging Stations in Smart Cities

The widespread use of electric vehicles necessitates meticulous planning for the placement of charging stations (CSs) in already crowded cities so that they can efficiently meet the charging demand while adhering to various real-world constraints such as the total budget, queuing time, electrical regulations, etc. Many classical and metaheuristic-based approaches provide good solutions, but they are not intuitive, and they do not scale well for large cities and complex constraints. Many classical solution techniques often require prohibitive amounts of memory and their solutions are not easily explainable. We analyzed the layouts of the 50 most populous cities of the world and observed that any city can be represented as a composition of five basic primitive shapes (stretched to different extents). Based on this insight, we use results from classical topology to design a new charging station placement algorithm. The first step is a topological clustering algorithm to partition a large city into small clusters and then use precomputed solutions for each basic shape to arrive at a solution for each cluster. These cluster-level solutions are very intuitive and explainable. Then, the next step is to combine the small solutions to arrive at a full solution to the problem. Here, we use a surrogate function and repair-based technique to fix any resultant constraint violations (after all the solutions are combined). The third step is optional, where we show that the second step can be extended to incorporate complex constraints and secondary objective functions. Along with creating a full software suite, we perform an extensive evaluation of the top 50 cities and demonstrate that our method is not only 30 times faster but its solution quality is also 36.62% better than the gold standard in this area—an integer linear programming (ILP) approach with a practical timeout limit.

Entire solutions to the parabolic Monge–Ampère equation with unbounded nonlinear growth in time

The Liouville type theorem on the parabolic Monge–Ampère equation −utdetD2u=1 states that any entire parabolically convex classical solution must be of form −t+|x|2/2 up to a re-scaling and transformation, under additional assumption that partial derivative with respect to time variable ut is strictly negative and bounded. In this paper, we study the case when ut is unbounded, prove an existence result of entire parabolically convex smooth solution and investigate the asymptotic behavior near infinity.

Mass concentration for Ergodic Choquard Mean-Field Games

We study concentration phenomena in the vanishing viscosity limit for second-order stationary Mean-Field Games systems defined in the whole space RN with Riesz-type aggregating coupling and external confining potential. In this setting, every player of the game is attracted toward congested areas and the external potential discourages agents to be far away from the origin. Assuming some restrictions on the strength of the attractive nonlocal term depending on the growth of the Hamiltonian, we study the asymptotic behavior of solutions in the vanishing viscosity limit. First, we obtain existence of classical solutions to potential-free MFG systems with Riesz-type coupling. Secondly, we prove concentration of mass around minima of the potential.

Accuracy evaluation of heat pulse method to determine ice thermal conductivity

The heat pulse (HP) method is among the most widely used methods to measure thermal properties of frozen soil, snow or glaciers. The phase change or ice melting caused by the released heat of the HP method considerably affects the measurement accuracy. Accurate estimation of thermal properties at high subfreezing soil temperatures (e.g., −5–0 °C) remains as a challenge for decades, given that ice melting effects are too complicated to be accounted in the analytical solutions to heat conduction equation. Ice is the fundamental component that determines hydrothermal properties of frozen soil and snow/ice. Therefore, this study observed the different thermal responses of the ice to 6 heating strategies for the heat pulse (combination of 2 heating durations and 3 heating strengths). Meanwhile, the results of finite element method based on COMSOL numerical simulations and two classical analytical solutions were compared. The results showed that accuracy of the results was improved by optimizing the phase change parameters of latent heat term that is included in the governing equation in COMSOL. The main findings are: (1) The numerical simulations and SLS (short-time linear heat source) method well fit the observed temperature change as a function of time at a distance from the heater, ΔT(r, t) curves, with differences in phase change temperatures; (2) Modification of phase change parameters in COMSOL considerably optimized the ΔT(r, t) curve for heating duration over 15 s; (3) The numerical method effectively improved the calculation accuracy of ice thermal conductivity by 9.66% at −5 °C to −1 °C and 17.53% at −3 °C to −1 °C, respectively.

Shear-induced wrinkling in accelerating thin elastic discs

The wrinkling instabilities produced by in-plane angular accelerations in a rotating disc are discussed here in a particular limit of relevance to very thin plates. By coupling the classical linear elasticity solution for this configuration with the Föppl–von Kármán plate buckling equation, a fourth-order boundary-value problem with variable coefficients is obtained. The singular-perturbation character of the resulting problem arises from a combination of factors encompassing both the pre-stress (due to the spinning motion) and the geometry of the annular domain. With the help of a simplified multiple-scale perturbation method in conjunction with matched asymptotics, we succeed in capturing the dependence of the critical (wrinkling) acceleration on the instantaneous speed of the disc as well as other physical parameters. We show that the asymptotic predictions compare well with the results of direct numerical simulations of the original bifurcation problem. The limitations of the formulae obtained are also considered, and some practical suggestions for improving their accuracy are suggested.

Anisotropic Fractional Cosmology: K-Essence Theory

In the particular configuration of the scalar field k-essence in the Wheeler–DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is β=2α2α−1. This fractional equation belongs to different intervals depending on the value of the barotropic parameter; when ωX∈[0,1], the order belongs to the interval 1≤β≤2, and when ωX∈[−1,0), the order belongs to the interval 0<β≤1. In the quantum scheme, we introduce the factor ordering problem in the variables (Ω,ϕ) and its corresponding momenta (ΠΩ,Πϕ), obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time T(τ); however, in the dust era we found a closed solution in the gauge time τ.

Best practices for portfolio optimization by quantum computing, experimented on real quantum devices

In finance, portfolio optimization aims at finding optimal investments maximizing a trade-off between return and risks, given some constraints. Classical formulations of this quadratic optimization problem have exact or heuristic solutions, but the complexity scales up as the market dimension increases. Recently, researchers are evaluating the possibility of facing the complexity scaling issue by employing quantum computing. In this paper, the problem is solved using the Variational Quantum Eigensolver (VQE), which in principle is very efficient. The main outcome of this work consists of the definition of the best hyperparameters to set, in order to perform Portfolio Optimization by VQE on real quantum computers. In particular, a quite general formulation of the constrained quadratic problem is considered, which is translated into Quadratic Unconstrained Binary Optimization by the binary encoding of variables and by including constraints in the objective function. This is converted into a set of quantum operators (Ising Hamiltonian), whose minimum eigenvalue is found by VQE and corresponds to the optimal solution. In this work, different hyperparameters of the procedure are analyzed, including different ansatzes and optimization methods by means of experiments on both simulators and real quantum computers. Experiments show that there is a strong dependence of solutions quality on the sufficiently sized quantum computer and correct hyperparameters, and with the best choices, the quantum algorithm run on real quantum devices reaches solutions very close to the exact one, with a strong convergence rate towards the classical solution, even without error-mitigation techniques. Moreover, results obtained on different real quantum devices, for a small-sized example, show the relation between the quality of the solution and the dimension of the quantum processor. Evidences allow concluding which are the best ways to solve real Portfolio Optimization problems by VQE on quantum devices, and confirm the possibility to solve them with higher efficiency, with respect to existing methods, as soon as the size of quantum hardware will be sufficiently high.

Global classical solvability and asymptotic behaviors of a parabolic-elliptic Chemotaxis-type system modeling crime activities

This paper is devoted to a two-dimensional parabolic-elliptic system in crime activities. The main difference between this system and the chemotaxis system with logarithmic singular sensitivity and quadratic logistic source is that the source term of this system is a mixtype quadratic term. The local existence of solutions to its intial boundary valve problem associated with homogeneous Neumann boundary conditions was considered by Rodríguez. The present study indicates that for any properly regular initial data there admits global classical solutions. Moreover, the qualitative behaviors of solutions in large time scales are considered as well.

The Spatial Arrangement of The Electric Field in the Needle-Plate Electrospinning

<p class="IJASEITAbtract">The electric field distribution of the Neddle-Plate (NP) electrospinning set up has reported due to the simple classical electrodynamics solutions. The charge is assumed to distribute uniformly in the needle (nozzle) and the collector (plate). The electric field has an influence only in the early stage of the electrospinning process. The electric field and the viscosity of the jet fluid have caused the bending of the straight jet. The high viscosity of the fluid can preserve the straight jet length much longer. The electric field gives the initial angular momentum of the jet due to the whipping motion of the jet. For the area away from the nozzle, the electric does not influence the whipping motion. Then the whipping motion solely due to the influence from the charge repulsion of the jet fluid and the evaporation of the solvent.</p>

Minimax regret stability in the graph model for conflict resolution

In strategic conflicts, decision-makers (DMs) do not constantly make their best decisions, which makes room for DMs to feel regretful. In this context, this work proposes the Minimax Regret Stability within the graph model for conflict resolution (GMCR) for modelling and analysing conflicts, considering that DMs would feel regret for an unsatisfactory decision. This concept does not require knowledge about the opponent’s preference in bilateral conflicts. The aim of the new solution concept is to recommend a state as stable if there exists a policy recommending to stay at that state which minimizes the maximum regret of the DM for a given conflict horizon, where a policy specifies what action a DM must choose in every conflict state. In addition, we investigate the relations among the Minimax regret stability and other classical GMCR solution concepts. Following, the influence of the horizon on the stability of states is also studied. Finally, a truckers’ strike conflict was used to illustrate how the new solution concept can provide valuable strategic insights in real-life conflict situations.

Optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market

This paper considers the issue of optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market. In our model, the price process is composed of a money market account and a default-free risky asset, assuming they rely on a stochastic economic factor described by a diffusion process. A defaultable perpetual bond is depicted by the reduced-form model, and both the default risk premium and the default intensity of it rely on the stochastic economic factor. Our goal is to maximize the infinite horizon expected discounted power utility of the consumption. Applying the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations and analyze them using the so-called sub-super solution method to prove the existence and uniqueness of their classical solutions. Next, we use a verification theorem to derive the explicit formula for optimal investment and consumption strategies. Finally, we provide a sensitivity analysis.

Fine-tuned YOLOv5 for real-time vehicle detection in UAV imagery: Architectural improvements and performance boost

Nowadays, Unmanned Aerial Vehicles (UAVs) have become useful for various civil applications, such as traffic monitoring and smart parkings, where real-time vehicle detection and classification is one of the key tasks. There are many challenges in detecting vehicles including small size objects and the variety in the UAV’s altitude and angle. As classic object detection solutions have limitations in confronting these challenges, recent methods are developed based on convolutional neural networks and their ability in effective feature learning. Due to the computational complexity in these networks and the need for accurate and real-time object detection, balancing the accuracy and inference speed is obligatory for efficiency. This paper aims to propose an accurate, efficient and real-time vehicle detection network based on the successful YOLOv5 object detection model. This is done by improving the structure of the model, adding attention mechanism and using an adaptive bounding box regression loss function. Also, considering the need for real-time inference speed, the depth and width of the model was balanced and ghost convolution was incorporated into the Neck unit to further improve the balance between accuracy and inference speed. The proposed method is evaluated on three different urban UAV imagery datasets, VisDrone, CARPK and VAID, specifically intended for civil applications. Comparing the obtained results from the proposed method with YOLOv5 baseline models, it achieved 3.52% higher mAP50 and 207.15% higher FPS than YOLOv5X on VisDrone dataset, while it is much smaller in size and GFLOPS. Totally, the proposed network outcomes show how the applied structural and conceptual modifications can upgrade the YOLO family towards being small in size, high in accuracy and fast in inference speed.

Anisotropy distorts the spreading of a fixed volume porous gravity current

We consider the release and subsequent gravity-driven spreading of a dense finite volume of fluid in an anisotropic porous medium bounded by an impermeable substrate. When the permeability in the vertical direction is much smaller than in the horizontal direction, as is the case in many real geological reservoirs, this restricts the spread of the current to a very thin layer near the impermeable base. Using a combination of asymptotic analysis and finite difference computations of Darcy flow, we show that there exist two distinct flow regimes. At early times, the bulk of the current descends slowly and uniformly, injecting fluid into thin finger-like regions near the base. At much later times, the current transitions to the classical gravity-driven solution and continues to spread with a self-similar shape. One interesting consequence is that the swept volume of the current grows differently depending on the anisotropy of the medium. This has important consequences for managing contaminant spills, where it is important to minimize the contacted volume of the aquifer, or during geological CO 2 sequestration where a larger contacted volume results in more CO 2 being stored.

Global classical solutions to the compressible Navier–Stokes equations with Navier-type slip boundary condition in 2D bounded domains

We study the barotropic compressible Navier–Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with C∞ boundary ∂Ω. By some new estimates on the boundary related to the Navier-type slip boundary condition, the classical solution to the initial-boundary-value problem of this system exists globally in time provided the initial energy is suitably small even if the density has large oscillations and contains vacuum states. Furthermore, we also prove that the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum (even a point) appears initially. As we known, this is the first result concerning the global existence of classical solutions to the compressible Navier–Stokes equations with Navier-type slip boundary condition and the density containing vacuum initially for general 2D bounded smooth domains.

On the relationship between the activity at point of interests and road traffic

The estimation and analysis of road traffic represent the preliminary steps towards satisfying the current needs for smooth, safe, and green transportation. Therefore, effective traffic monitoring is an essential topic alongside the planning of sustainable transportation systems and the development of new traffic management concepts. In contrast to classical traffic detection solutions, this study investigates the correlation between travelers' social activities and road traffic. The s's primary goal is to investigate the presence of the relationship between social activity and road traffic, which might allow an infrastructure-independent traffic monitoring technique as well. People's general activities at Point of Interest (POI) locations (measured as occupancy parameter) are correlated with traffic data so that, finally, proper proxys can be defined for link-level average traffic speed estimation. The method is tested and evaluated using real-world traffic and POI occupancy data from Budapest (District XI.). The results of the correlation investigation justify an indirect relationship between activity at POIs and road traffic, which holds promise for future practical applicability.

Investigation of the Weak Solvability of One Viscoelastic Fractional Voigt Model

This article is devoted to the investigation of the weak solvability to the initial boundary value problem, which describes the viscoelastic fluid motion with memory. The memory of the fluid is considered not at a constant position of the fluid particle (as in most papers on this topic), but along the trajectory of the fluid particle (which is more physical). This leads to the appearance of an unknown function z, which is the trajectory of fluid particles and is determined by the velocity v of a fluid particle. However, in this case, the velocity v belongs to L2(0,T;V1), which does not allow the use of the classical Cauchy Problem solution. Therefore, we use the theory of regular Lagrangian flows to correctly determine the trajectory of the particle. This paper establishes the existence of weak solutions to the considered problem. For this purpose, the topological approximation approach to the study of mathematical hydrodynamics problems, constructed by Prof. V. G. Zvyagin, is used.

On Local Unique Solvability for a Class of Nonlinear Identification Problems

Nonlinear identification problems for evolution differential equations, solved with respect to the highest-order Dzhrbashyan–Nersesyan fractional derivative, are studied. An equation of the considered class contains a linear unbounded operator, which generates analytic resolving families for the corresponding linear homogeneous equation, and a continuous nonlinear operator, which depends on lower-order Dzhrbashyan–Nersesyan derivatives and a depending on time unknown element. The identification problem consists of the equation, Dzhrbashyan–Nersesyan initial value conditions and an abstract overdetermination condition, which is defined by a linear continuous operator. Using the contraction mappings theorem, we prove the unique local solvability of the identification problem. The cases of mild and classical solutions are studied. The obtained abstract results are applied to an investigation of a nonlinear identification problem to a linearized phase field system with time dependent unknown coefficients at Dzhrbashyan–Nersesyan time-derivatives of lower orders.

Implementation of Remote Control for the AM 524 Antenna Amplifier Unit System in SAC Chambers

In the rapidly evolving landscape of modern technology, particularly in telecommunications and pervasive computerization across diverse sectors, the value of information has soared, becoming the linchpin of success in politics and business alike. With the majority of information now flowing through various computing devices, safeguarding them from unauthorized interception has assumed paramount importance. A critical threat in this context emanates from unintentional electromagnetic emissions generated by these devices. Under favorable conditions, these emissions can be exploited by unauthorized entities to reconstruct processed information, a phenomenon known as electromagnetic infiltration. Such emissions, correlated with useful information and conducive to its reconstruction, are termed revealing emissions, with the enabling process labelled as electromagnetic information leakage. This article presents the design and construction of a remote control system for managing antenna amplifier blocks within the AM 524 antenna system, dedicated to investigating information leakage from multimedia devices. The system facilitates remote switching of the five inputs on antenna amplifiers GX 525, GX 526, and GX 527 from a PC, utilizing specialized software. The authors provide an overview of the AM 524 antenna system, elucidate the design concept behind the remote control system, and highlight the central component—the ADAM 6052 module. Additionally, the article introduces the controlling software. It encompasses the device’s construction, including component details, connection schematics, and images of the assembled system, along with a verification process confirming its operational accuracy. Furthermore, the article outlines the application of the proposed solution in assessing the effectiveness of shielding within SAC chambers, employing the measurement methodology specified in accordance with the EN 50147-1:1996 standard. This additional information underscores the practical utility and relevance of the presented remote control system in the context of electromagnetic shielding evaluation for secure environments. Additionally, to assess the effectiveness of the proposed commutator solution, measurements were conducted to evaluate the shielding efficiency of the SAC chamber using a modified coaxial cable. The results of the shielding efficiency of the SAC chamber measurements for the proposed and classical solutions are also presented.