Maxwell Type Research Articles

Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and Their Applications

Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and Their Applications

Bandgap structure of tensegrity mass–spring chains equipped with internal resonators

This work studies the dispersion relation of a Maxwell type mass–spring chain formed by lumped masses and the parallel arrangement of two different types of tensegrity prisms. Use is made of the Bloch–Floquet theory of discrete systems in association with a linearized model of the response of the tensegrity units under compression loading. Such a modeling is aimed at studying the propagation of compression waves under small perturbations of the initial equilibrium state of the system. For a given value of the cable’s prestress, the tensegrity systems connecting the lumped masses react as elastic springs, which exhibit axial deformations accompanied by relative twisting rotations of the terminal bases. The twisting motion of the chain affects the expression of the kinetic energy, and is accounted for by introducing a suitable definition of equivalent masses. The bandgap structure of the analyzed system is analytically determined and numerical results are obtained for a chain formed by physical models tensegrity θ=1 prisms aligned in parallel with minimal tensegrity prisms. The given results highlight the highly tunable frequency bandgap properties of tensegrity mass–spring chains exhibiting internal resonance capabilities.

Klein–Gordon–Maxwell Equations Driven by Mixed Local–Nonlocal Operators

Classical results concerning Klein–Gordon–Maxwell type systems are shortly reviewed and generalized to the setting of mixed local–nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real parameter. In this paper, we provide a range of parameter values to ensure the existence of solitary (standing) waves, obtained as Mountain Pass critical points for the associated energy functionals in two different settings, by considering two different classes of potentials: constant potentials and continuous, bounded from below, and coercive potentials.

Enhancing heat transfer in solar-powered ships: a study on hybrid nanofluids with carbon nanotubes and their application in parabolic trough solar collectors with electromagnetic controls

The aim of this research is to explore the use of solar-powered ships (SPS) as a means to reduce greenhouse gas emissions and fossil fuel dependency in the maritime industry. The study focuses on improving the heat transfer efficiency in SPS by employing hybrid nanofluids (HNF) containing carbon nanotubes (CNTs). Additionally, a novel approach utilizing renewable energy and electromagnetic control is proposed to enhance the performance of SPS. The research implements the non-Newtonian Maxwell type and Cattaneo–Christov heat flux model in parabolic trough solar collectors used for ships. The study conducts theoretical experiments and simulations to evaluate the thermal conductivity and viscosity of the CNT-based HNF. Various properties, including solar thermal radiation, viscous dissipation, slippery velocity, and porous media, are assessed to determine the effectiveness of thermal transport in SPS. The research employs similarity variables to simplify the complex partial differential equations into ordinary differential equations and solves them using the Chebyshev collocation spectral method. The results indicate that the MWCNT-SWCNT/EO hybrid nanofluid significantly improves the thermal conductivity, thereby enhancing heat transfer. The HNF exhibits an efficiency rate of approximately 1.78% with a minimum efficiency rate of 2.26%.

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.

A phase field model for fractures in ice shelves

AbstractIce shelves are large floating ice masses, that are formed when glaciers are becoming afloat at the margin of ice sheets. One dominating mass loss mechanism of ice shelves is calving, describing the detachment of icebergs at the front. Ice shelves stabilize inland ice glaciers due to buttressing. If the stabilizing effect of an ice shelf vanishes because of disintegration or thinning, the corresponding glacier accelerates resulting in sea level rise.To describe calving and disintegration of ice shelves, it is important to investigate fracture propagation in ice. A powerful method in fracture mechanics is the phase field method which is based on Griffith's theory. It approximates cracks in a diffuse manner by using a continuous scalar field. We propose a phase field fracture model for ice considering its characteristic material properties. The material behavior of ice depends on the considered time scales. On short time scales it behaves like a solid and while it acts like a fluid on long time scales, which classifies it as a viscoelastic material of Maxwell type. This has been verified by observations. The phase field method allows us to simulate typical fracture situations of ice shelves in Antarctica and Greenland.

A bridge on Lomnitz type creep laws via generalized fractional calculus

This paper is dedicated to achieving the unification of the scattered Lomnitz type creep laws. Thereupon, a novel generalized fractional calculus, that is, Katugampola-like fractional calculus is well-defined and employed as an effective tool, along with some fundamental qualities as by-products. By virtue of the hereditary theory of viscoelasticity and Volterra integral equation method, a compatible stress-strain relation with memory effects and time-varying viscosity established results in a unified Lomnitz creep law. Then, a comparative analysis on the creep function and relaxation function inherited from the unified Lomnitz creep law is exhibited via reasoning and numerical simulation. Besides, physical interpretation of such unified Lomnitz creep law is also provided with the aid of the modified spring-dashpot model of Maxwell type. Results carried out in this paper might provide a full characterization of the creep of igneous rocks to meet some special theoretical and experimental requirements.

Formation of singularities for one-dimensional relaxed compressible Navier-Stokes equations

We investigate the formation of singularities in one-dimensional hyperbolic compressible Navier-Stokes equations, a model proposing a relaxation leading to a hyperbolization through a nonlinear Cattaneo law for heat conduction as well as through the constitutive Maxwell type relations for the stress tensor. By using the entropy dissipation inequality, which gives the lower energy estimates of the local solutions without any smallness condition on initial data, and by constructing some useful averaged quantities we show that there are in general no global C1 solutions for the studied system with some large initial data.This appears as a remarkable contrast to the situation without relaxation, i.e. for the classical compressible Navier-Stokes equations, where global large solutions exist. It also contrasts the fact that for the linearized system associated to the classical resp. relaxed compressible Navier-Stokes equations, the qualitative behavior is exactly the same: exponential stability in bounded domains and polynomial decay without loss of regularity for the Cauchy problem.

Carroll Symmetry, Dark Energy and Inflation

Carroll symmetry arises from Poincaré symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state E+P=0 for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with w = − 1. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry. To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.

Thermo-viscoelastic homogenization of 3D woven composites with time-dependent expansion coefficients

Stress relaxation in the viscoelastic matrix influences the evolution of thermal expansion and chemical shrinkage of polymer composites. Its effects are included into a viscoelastic model of the generalized Maxwell type by means of time-dependent thermal expansion and chemical shrinkage coefficients. A homogenization strategy is proposed to obtain these coefficients of the composite from the constituent behaviors, taking into account the viscoelastic effects. The homogenized behavior is validated by full-scale finite element simulations. It reproduces features such as sign changes of the thermal strain rate close to the glass transition temperature and thermal creep effects, which can have an important impact on the residual stress formation in composites, but are not taken into account by classical thermo-elastic homogenization methods.

Some Results About the Structure of Primitivity Domains for Linear Partial Differential Operators with Constant Coefficients

Let G(D) be a linear partial differential operator on {mathbb {R}}^n, with constant coefficients. Moreover let Omega subset {mathbb {R}}^n be open and Fin L^1_{text {loc}} (Omega , {mathbb {C}}^N). Then any set of the form Af,F:={x∈Ω|(G(D)f)(x)=F(x)},withf∈Wlocg,1(Ω,Ck)\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} A_{f,F}:= \\{ x\\in \\Omega \\, \\vert \\, (G(D)f)(x)=F(x)\\}, \\text { with }f\\in W^{g,1}_{\\text {loc}}(\\Omega , {\\mathbb {C}}^k) \\end{aligned}$$\\end{document}is said to be a G-primitivity domain of F. We provide some results about the structure of G-primitivity domains of F at the points of the (suitably defined) G-nonintegrability set of F. A Lusin type theorem for G(D) is also provided. Finally, we give applications to the Maxwell type system and to the multivariate Cauchy-Riemann system.

Thermal Characterization of Coolant Maxwell Type Nanofluid Flowing in Parabolic Trough Solar Collector (PTSC) Used Inside Solar Powered Ship Application

Parabolic trough solar collectors (PTSCs) are generally utilized to reach high temperatures in solar-thermal applications. The current work investigates entropy production analysis and the influence of nano solid particles on a parabolic trough surface collector (PTSC) installed within a solar powered ship (SPS). For the current investigation, the non-Newtonian Maxwell type, as well as a porous medium and Darcy–Forchheimer effects, were used. The flow in PTSC was produced by a nonlinear stretching surface, and the Cattaneo–Christov approach was used to assess the thermal boundary layer’s heat flux. Similarity transformation approach has been employed to convert partial differential equations into solvable ordinary differential equations allied to boundary conditions. Partial differential and the boundary conditions have been reduced into a group of non-linear ordinary differential equations. A Keller-box scheme applied to solve approximate solutions of the ordinary differential equations. Single-walled carbon nanotubes -engine oil (SWCNT-EO) and Multiwalled carbon nanotubes/engine oil (MWCNT-EO) nanofluids have been utilized as working fluid. According to the findings, the magnetic parameter led to a reduction in the Nusselt number, as well as an increment in skin friction coefficient. Moreover, total entropy variance over the domain enhanced for flow rates through Reynolds number and viscosity fluctuations were monitored by using Brinkman number. Utilizing SWCNT-EO nanofluid increased the thermal efficiency between 1.6–14.9% in comparison to MWCNT-EO.

Interaction among neighbouring rectangular finite strike slip faults in a linear viscoelastic half space representing lithosphere-asthenosphere system

There are seismically active regions consisting of fault system with a number of neighbouring earthquake faults. A movement across any one of them may affect the nature of stress accumulation near the others. Mathematical models may be developed to study these interactions and the pattern of interseismic stresses during the aseismic period in between two consecutive seismic events. In this paper, the lithosphere-asthenosphere system is being represented by a linear viscoelastic half space. The material of the half space is expected to possess the properties of both Maxwell and Kelvin type materials. It is assumed that the system is under a steady shear stress generated by some tectonic phenomena. For obtaining the solution for displacement, strain and stresses from the resulting boundary value problem, Integral transform, Green’s function techenique and correspondence principle have been used. Appropriate estimates of the model parameters were used in carrying out the numerical computations for investigating the nature of interactions among the faults.

Symmetric U(1) and Z2 spin liquids on the pyrochlore lattice

The geometrically frustrated 3D pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a $\mathrm{U(1)}$ quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. In this work, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric $\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 $\mathrm{U(1)}$ spin liquids and 28 $\mathbb{Z}_2$ spin liquids that preserve pyrochlore space group symmetry while, upon further imposing time reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several $\mathrm{U(1)}$ spin liquid classes possess an unusual gapless multi-nodal-line structure ("nodal star") in the spinon bands, which is protected by the projective actions of the three-fold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form $C/T\sim \sqrt{T}+\sqrt{T}/\ln T$, in contrast to the form $C/T \sim T^2$ of the standard $\mathrm{U(1)}$ pyrochlore spin liquid with gapped spinons.

On Hr(curl,Ω) estimates for a Maxwell type system in convex domains

In bounded convex domains, the regularity of a vector field u with its divu, curlu in Lr space and the tangential component or the normal component of u over the boundary in Lr space, is established for 1<r<∞. As an application, we derive an Hr(curl,Ω) estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space Hr(curl,Ω) for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal.

Liouville theorems for nonnegative solutions to static weighted Schrödinger–Hartree–Maxwell type equations with combined nonlinearities

In this paper, we are concerned with the physically interesting static weighted Schrodinger–Hartree–Maxwell type equations $$\begin{aligned} (-\Delta )^{\frac{\alpha }{2}}u(x)=c_{1}|x|^{a}\left( \frac{1}{|x|^{\sigma }}*|u|^{q_{1}}\right) u^{p_{1}}(x)+c_{2}|x|^{b}u^{p_{2}}(x) \quad \text {in} \quad \mathbb {R}^{n} \end{aligned}$$ with combined nonlinearities, where $$n\ge 2$$ , $$0<\alpha \le 2$$ , $$0<\sigma <n$$ , $$c_{1}, \, c_{2}\ge 0$$ with $$c_{1}+c_{2}>0$$ , $$0\le a,b<+\infty $$ , $$0<q_{1}\le \frac{2n-\sigma }{n-\alpha }$$ , $$0<p_{1}\le \frac{n+\alpha -\sigma +2a}{n-\alpha }$$ and $$0<p_{2}\le \frac{n+\alpha +2b}{n-\alpha }$$ . We derive Liouville theorems (i.e., non-existence of nontrivial nonnegative solutions) in the subcritical cases (see Theorem 1.1). The argument used in our proof is the method of scaling spheres developed in Dai and Qin (Liouville type theorems for fractional and higher order Henon–Hardy equations via the method of scaling spheres, arXiv:1810.02752 ). As a consequence, we also derive Liouville theorem for weighted Schrodinger–Hartree–Maxwell type systems. Our results extend the Liouville theorems in Dai and Liu (Calc Var Partial Differ Equ 58(4): Paper No. 156, 24 pp, 2019) and Dai et al. (Classification of nonnegative solutions to static Schrodinger–Hartree–Maxwell type equations, arXiv:1909.00492 ) for $$0<\alpha \le 2$$ .

A multilevel zero-inflated Conway–Maxwell type negative binomial model for analysing clustered count data

Basic negative binomial models can only capture over-dispersed count responses, because the variance of the distribution is always greater than the mean value. So, they are not the best selection when the data are under-dispersed or have less dispersion than the negative binomial. Over the last years, a variety of new distributions that can account a wide range of dispersion in count data, have been introduced. One of these novel distributions is Conway–Maxwell type negative binomial distribution. In biomedical studies, it is common to demonstrate excess zeros and a pattern of dispersion in count data. Also, the observations may be correlated in clusters or longitudinally. Here, we propose a multilevel zero-inflated Conway–Maxwell type negative binomial model. Statistical inference is employed via an expectation-maximization algorithm for the parameter estimation. The model performance is illustrated by simulation studies and with a real data set.

Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations

In this paper, we are mainly concerned with the physically interesting static Schr\"{o}dinger-Hartree-Maxwell type equations \begin{equation*} (-\Delta)^{s}u(x)=\left(\frac{1}{|x|^{\sigma}}\ast |u|^{p}\right)u^{q}(x) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} involving higher-order or higher-order fractional Laplacians, where $n\geq1$, $0<s:=m+\frac{\alpha}{2}<\frac{n}{2}$, $m\geq0$ is an integer, $0<\alpha\leq2$, $0<\sigma<n$, $0<p\leq\frac{2n-\sigma}{n-2s}$ and $0<q\leq\frac{n+2s-\sigma}{n-2s}$. We first prove the super poly-harmonic properties of nonnegative classical solutions to the above PDEs, then show the equivalence between the PDEs and the following integral equations \begin{equation*} u(x)=\int_{\mathbb{R}^n}\frac{R_{2s,n}}{|x-y|^{n-2s}}\left(\int_{\mathbb{R}^{n}}\frac{1}{|y-z|^{\sigma}}u^p(z)dz\right)u^{q}(y)dy. \end{equation*} Finally, we classify all nonnegative solutions to the integral equations via the method of moving spheres in integral form. As a consequence, we obtain the classification results of nonnegative classical solutions for the PDEs. Our results completely improved the classification results in \cite{CD,DFQ,DL,DQ,Liu}. In critical and super-critical order cases (i.e., $\frac{n}{2}\leq s:=m+\frac{\alpha}{2}<+\infty$), we also derive Liouville type theorem.

Dual Hysteresis Model of MR Dampers

This study concerns modeling the hysteretic behaviour of magnetorheological (MR) dampers. In general, hysteresis is one of key factors influencing the output of such actuators. So far more attention of various researchers has been paid to studying the combined hysteretic behaviour of MR actuators by observing the relationships between the output (force/torque) and the inputs (current, velocity, position). However, these devices feature two distinct hysteretic mechanisms: mechanical/hydraulic and magnetic. The mechanical hysteresis is of different nature than the magnetic hysteresis due to the properties of ferromagnetic materials forming the actuator's elec- tromagnet circuit, and these should be split in the modeling process. In the present study we separate the magnetic hysteresis from the mechanical/hydraulic one by investigating the magnetic flux vs exciting current relationship of a commercial flow-mode MR damper subjected to sinusoidal current loading and independently of the mechanical excitations. The resulting behaviour of the electromagnetic circuit is then examined using the nonlinear inductor approach with hysteresis. Total hysteresis is then modeled using a non-linear inductor model in combination with a phenomenological parametric Maxwell type model of the damper.

Torsional Vibration Analysis of Carbon Nanotubes Using Maxwell and Kelvin-Voigt Type Viscoelastic Material Models

Torsional dynamic analysis of viscoelastic Carbon Nanotubes (CNT) has been carried out in the present work. Maxwell and Kelvin-Voigt type viscoelasticity are considered in the modeling of viscoelastic material. Nonlocal Elasticity Theory is used in the formulation of governing equation of motion and boundary conditions. Viscoelasticity and nonlocal effects of structure on the free torsional vibration of CNTs have been investigated. Clamped-clamped and clamped-free boundary conditions are considered. Present study results could be useful in design of nano-medicine delivery applications.