Finite Speed Research Articles

EnVarA-FEM for the flux-limited porous medium equation

The flux-limited porous medium equation is a kind of nonlinear degenerate parabolic equation based on the porous medium equation, its solution not only has a finite propagation speed and possible waiting time, but also may develop jump fronts. It is difficult to construct numerical methods to capture these features in an effective way. We propose structure-preserving finite element numerical schemes based on the energetic variational approach, which are proved to be uniquely solvable, positivity preserving and energy dissipative. The analysis of the free boundaries conditions is given to illustrate the circumstances under which the solution of the flux-limited porous medium equation will have finite propagation speed, waiting time or jump fronts. Moreover, the optimal convergence analysis for the nonlinear numerical scheme is presented by applying the technique of combining the rough and refined error estimates. Numerical experiments reveal that the proposed numerical method can successfully capture important features of the flux-limited PME: finite propagation speed of the free boundary, waiting time, effect of amplitudes on the regularity of the solutions and jump fronts. In particular, the waiting time is computed naturally and the convergence order of the waiting time can be given numerically. A criterion to approximate the time where discontinuous interfaces occur is also established, and the corresponding convergence order is given numerically.

Korteweg-Type Fluids and Thermodynamic Modelling via Higher-Order Gradients

This paper investigates the modelling of Korteweg-type fluids and hence the dependence of the stress tensor on gradients of mass density. This topic, originating from the need for describing capillarity effects, is mainly of interest in connection with nanosystems where the mean free path may be comparable with the geometric dimensions of the system. In addition to the Korteweg fluid model, the paper gives a review of the stress tensor function arising in quantum fluid hydrodynamics. Next, thermodynamic consistency is established for a fluid involving first- and second-order density gradients. The modelling investigated is a generalization of the classical Korteweg fluid and allows a better understanding of previous thermodynamic restrictions. The restrictions determined for the general scheme with second-order gradients are applied to the particular cases of the Korteweg fluid and the quantum fluid. Further, to allow for discontinuity wave solutions with finite speed of propagation, a model is established which involves higher-order derivatives and reduces to the Korteweg fluid in stationary conditions.

Finite-Time Control for Dual Three-Phase Hybrid Excitation Synchronous Machine Based on Torque Sensorless Current Coordinative Strategy

In this paper, the finite time speed regulation problem is investigated for a dual three-phase hybrid excitation synchronous machine (DTP-HESM) without a torque meter. The electromagnetic torque estimation required in the current coordinative strategy is obtained through the disturbance estimation technology. This method increases fault tolerance and reduces the cost as well as complexity of the DTP-HESM system. In contrast to the existing controllers in the speed loop, the non-singular terminal sliding mode control method is adopted to ensure the finite-time convergence of speed tracking in the whole speed region. To achieve better dynamic performance in the presence of lumped disturbances, including unknown load torque and unmodeled dynamics, the disturbance estimations are introduced into the sliding mode variable to establish a composite speed regulating controller. Simulations and experiments are carried out to validate the feasibility and effectiveness of the proposed control scheme.

Bioheat Transfer with Thermal Memory and Moving Thermal Shocks

This article investigates the effects of thermal memory and the moving line thermal shock on heat transfer in biological tissues by employing a generalized form of the Pennes equation. The mathematical model is built upon a novel time-fractional generalized Fourier’s law, wherein the thermal flux is influenced not only by the temperature gradient but also by its historical behavior. Fractionalization of the heat flow via a fractional integral operator leads to modeling of the finite speed of the heat wave. Moreover, the thermal source generates a linear thermal shock at every instant in a specified position of the tissue. The analytical solution in the Laplace domain for the temperature of the generalized model, respectively the analytical solution in the real domain for the ordinary model, are determined using the Laplace transform. The influence of the thermal memory parameter on the heat transfer is analyzed through numerical simulations and graphic representations.

Is a wet-bulb temperature of 35 ∘C the correct threshold for human survivability?

A wet-bulb temperature of 35 ∘C is widely used as the threshold for human survivability, but the wet-bulb temperature is not a particularly accurate metric for human heat stress. For a person in the shade, a more accurate metric is the heat index, which is based on a model of human thermoregulation that accounts for metabolic heat, radiation, respiratory ventilation, and finite wind speeds. The heat index has two critical values: the highest heat index for which a healthy core temperature can be maintained and the highest heat index that is survivable. It is shown here that a wet-bulb temperature of 35 ∘C corresponds to conditions between these two critical values. For example, in a world warmer than pre-industrial by 10 ∘C, about 30% of the world’s population would be exposed once or more per year to a wet-bulb temperature above 35 ∘C, but the heat index reveals that less than 2% would be exposed to fatal conditions while over 60% would be exposed to conditions that would cause hyperthermia.

A peridynamic model for coupled thermo-mechanical-oxygenic analysis of C/C composites with SiC coating

The oxidation induced by coating cracking is a general failure mode of high-temperature composites such as C/C and C/SiC. However, this failure mode has not been fully investigated due to the lack of a method suitable for both crack simulation and oxidation interface capture. In this paper, a coupled thermo-mechanical-oxygenic peridynamic model is proposed for SiC-coated C/C composites in an oxidizing environment. The ordinary state-based peridynamics is extended to plane strain thermoelastic problems for orthotropic media to calculate the crack distribution. Cracks in the coating are modeled as oxygen diffusion channels and the peridynamic oxidation equation is developed to simulate the oxidation of the C/C substrate. Furthermore, the peridynamic non-Fourier heat transfer equation is employed to consider the finite thermal propagation speed and the model is validated by experimental results. Numerical examples are presented to investigate the oxidation failure after thermal shock, non-Fourier thermal shock fracture, and stress oxidation failure of SiC-coated C/C composites.

Basic Properties of Solutions of Boundary Value Problem for the Dirac-Wave Operator

We study local and global properties of solutions of the boundary value problem for the Dirac wave operator. This includes explicit formulas, domain of dependence, range of influence, finite propagation speed and energy estimates. We also introduce the space of Dirac wave homogeneous polynomials and the corresponding Dirac-wave conjugate functions.

An optimal fog-cloud offloading framework for big data optimization in heterogeneous IoT networks

Executing complex and time-sensitive operations has become difficult due to the increased acceptance of Internet of Things (IoT) devices and IoT-generated big data, which can result in problems with power consumption and lag time. The fog computing layer is a distributed computing option that can handle some of these issues. However, fog computing devices’ limited computing and power capabilities make it difficult to complete operations under time constraints while minimizing service latency and fog resource energy consumption in delay-sensitive IoT-Fog applications. This paper suggests a dynamic integer linear programming technique for facilitating optimal task offloading that distributes resources from the fog computing layer to IoT devices while considering the constraints on timely task execution and resource availability. The offloading challenge is modeled as an integer linear programming (ILP) problem to ease the burden on finite fog resources and speed up the completion of time-sensitive operations. Given the large dimensionality of tasks in a dynamic environment, a task prioritization method is adopted to minimize tasks’ latency and the energy consumption of fog nodes. The findings demonstrate that the suggested approach performs better than benchmark approaches regarding energy utilization and service latency. Overall, the proposed technique offers an efficient and practical response to the issues raised by IoT devices and fog computing while enhancing system efficiency regarding power consumption and latency.

Development and validation of a software application to analyze thermal and kinematic multimodels of Stirling engines

The work developed presents, for the first time, a tool to analyze all the thermodynamic models used in the study and development of Stirling engines: isothermal, ideal adiabatic and adiabatic with losses, combined adiabatic thermodynamic with finite speed (CAFS), thermodynamic with finite speed (FST), ideal polytropic and polytropic with losses (PSVL), allowing a comparative study of them.This software (ASCE-UMA), designed and implemented in a Matlab GUI® allows to obtain the operating parameters of these engines, calculating the thermodynamic parameters, power output and efficiency. Additionally, the thermodynamic models can be evaluated with different mechanical configurations, for which different drive mechanisms are implemented: Sinusoidal, Alfa Ross yoke types, Alfa Ross V yoke, Beta rhombic type and free piston Stirling engine (FPSE). Thermoacoustic and other, models could be analyzed by virtue of their similarity of movement with some of the implemented models. In the same way, ASCE-UMA allows the study of various exchanger configurations, as well as various regenerator models. The versatility of ASCE-UMA allows the development analysis of all the fundamental elements of a new prototype as well as the analysis of experimental data by performing a customized and detailed calculation. To test the effectiveness of ASCE-UMA, its performance is verified by analyzing Ross Yoke D-90 models and a GM GPU-3 engine.This is a tool that allows to analyze and comparing the different models and the different existing mechanisms for the multiple configurations of Stirling engines in an easy and intuitive application with a high-quality graphical interface.

Thermoelastic diffusion system of type II with nonlocal delay

This article deals with the well-posedness and exponential stability of a thermoelastic diffusion system with delay under Green and Naghdi’s theory that predicts a finite speed for heat propagation and involves no energy dissipation. Through semigroup theory, we prove the well-posedness by the Lumer–Phillips theorem and the exponential stability by exploring the dissipative properties of the linear operator associated with the model using the Gearhart–Huang–Pruss theorem.

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heating on a “nanoscale” plate is considered. The focus is on the anomalous heat transfer mechanisms that result from anomalous diffusion of hot electrons and are characterized by retarded thermal conduction, accelerated thermal conduction, or transition from super-thermal conductivity in the short-time response to sub-thermal conductivity in the long-time response and described by the fractional Jeffreys equation with three fractional parameters. The recent double-strip problem, Awad et al., Eur. Phy. J. Plus 2022, allowing the overlap between two propagating thermal waves, is generalized from the semi-infinite heat conductor case to thermoelastic case in the finite domain. The elastic response in the material is not simultaneous (i.e., not Hookean), rather it is assumed to be of the Kelvin–Voigt type, i.e., σ=Eε+τεε˙, where σ refers to the stress, ε is the strain, E is the Young modulus, and τε refers to the strain relaxation time. The delayed strain response of the Kelvin–Voigt model eliminates the discontinuity of stresses, a hallmark of the Hookean solid. The immobilization of thermal conduction described by the ordinary Jeffreys equation of heat conduction is salient in metals when the heat flux precedence is considered. The absence of the finite speed thermal waves in the Kelvin–Voigt model results in a smooth stress surface during the heating process. The temperature contours and the displacement vector chart show that the anomalous heat transfer characterized by retardation or crossover from super- to sub-thermal conduction may disrupt the ultrafast laser heating of metals.

High-frequency magnetohydrodynamics

We consider the case that the displacement current is not neglected in the classical MHD equations, as it is usually done. This amounts to cast them in the relativistic framework of a finite speed of light. We show some consequences in describing magnetic reconnection phenomena and for hydromagnetic waves. In the first case, the equation for the magnetic induction is changed from (formally) parabolic to (formally) hyperbolic, in the second case both, the perturbed magnetic field and the particle velocity, obey to a certain third-order in time partial differential equation, rather than to the classical wave equation. We stress the role of two typically small but nonzero parameters, the magnetic diffusivity, η (corresponding to large values of the Lundquist number), and ε:=c−2.

A generic instability in clustering dark energy?

In this paper, we study the effective field theory (EFT) of dark energy (DE) for the k-essence model beyond linear order. Using particle-mesh N-body simulations that consistently solve the DE evolution on a grid, we find that the next-to-leading order in the EFT expansion, which comprises the terms of the equations of motion that are quadratic in the field variables, gives rise to a generic instability in the regime of low speed of sound (high Mach number). We rule out the possibility of a numerical artefact by considering simplified cases in spherically and plane symmetric situations analytically. If the speed of sound vanishes exactly, the non-linear instability makes the evolution singular in finite time, signalling a breakdown of the EFT framework. The case of finite (but small) speed of sound is subtle, and the local singularity could be replaced by some other type of behaviour with strong non-linearities. While an ultraviolet completion may cure the problem in principle, there is no reason why this should be the case in general. As a result, for a large range of the effective speed of sound cs , a linear treatment is not adequate.

Land cover aware temperature correction of bicycle transects: A case study of mapping the air temperature in two Belgian cities

A low-threshold methodology for mapping the nocturnal air temperature in an urbanized region based on bicycle measurements and a number of in-situ weather stations is presented. Firstly, two corrections are applied on the bike measurements: a thermal inertia correction to account for the finite reaction speed of the temperature sensor and a temperature decline correction to offset the background temperature evolution during the mobile measurements. The latter includes for the first time land cover information to account for its impact on the nocturnal cooling rate. Secondly, a linear statistical model is used to produce regional maps of the air temperature based on the relationship between the corrected temperature and land cover around the bicycle transect. Applying this methodology on the Belgian cities of Antwerp and Ghent demonstrates that this low-threshold approach allows for a comprehensive picture of the air temperature and that it has advantages compared to more traditional decline corrections. Further improvements could be made by employing more accurate temperature sensors, applying more complex statistical models and performing multiple measurement campaigns per evening.

A Covariant Non-Local Model of Bohm's Quantum Potential.

Assuming that the energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm's quantum potential and the Madelung equation are obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics do admit a classical interpretation based on non-locality. Here, we generalize this approach imposing a finite speed of propagation of any perturbation, thus determining a covariant formulation of the Madelung equation.

Oscillations of the Earth Surface Caused by Its Rotation, Motion Around the Sun, and a Finite Speed of Gravity

Oscillations of the Earth Surface Caused by Its Rotation, Motion Around the Sun, and a Finite Speed of Gravity

Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation

We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation c > 0 {\mathfrak {c}}>0 under minimal (i.e., necessary) assumptions on the influence function. In particular, we assume that the influence function is globally positive, which is necessary for reaching global consensus, and such that the agents move with speeds strictly less than c {\mathfrak {c}} , which is necessary for well-posedness of solutions. From this point of view, our result is optimal. The proof is based on the fact that the state-dependent delay, induced by the finite speed of information propagation, is uniformly bounded.

On the Relation of One-Dimensional Diffusions on Natural Scale and Their Speed Measures

It is well known that the law of a one-dimensional diffusion on natural scale is fully characterized by its speed measure. Stone proved a continuous dependence of such diffusions on their speed measures. In this paper we establish the converse direction, i.e., we prove a continuous dependence of the speed measures on their diffusions. Furthermore, we take a topological point of view on the relation. More precisely, for suitable topologies, we establish a homeomorphic relation between the set of regular diffusions on natural scale without absorbing boundaries and the set of locally finite speed measures.

Finite time and finite speed thermodynamic optimization for an irreversible Atkinson cycle

Combining the finite piston speed thermodynamics and finite time thermodynamics and considering the irreversible losses caused by heat transfer, friction, finite piston speed and internal irreversibility, a more practical irreversible Atkinson cycle model is founded in the paper. When the finite piston speeds in cycle processes are not equal, choosing the ecological coefficient of performance, thermal efficiency, power output and ecological function as performance parameters, and choosing the piston speed ratio and finite piston speed as the design parameters, the relationships among the performance parameters and design parameters are obtained, and the influences of the finite piston speed and piston speed ratio on the performance parameters are presented. The research results show that it is necessary to consider the different piston speeds in each process. The designer can choose the corresponding ranges of design parameters to make the corresponding performance parameter reach the maximum value in practice. This work has a certain theoretical significance and can guide the practical design.

Problem of Longitudinal Vibrations of a Viscoelastic Rod of Maxwell Type

In this paper, we study well-posedness in the sense of Hadamard of the Cauchy problem for a one-dimensional hyperbolic system of partial differential equations describing the longitudinal vibrations of a viscoelastic rod of Maxwell type with constant cross-section. We discuss some properties of the system and its solutions: the conservation of modified “energy”, the finite propagation speed, dispersion, and dissipation of solutions.