Nonsingular Behavior Research Articles

Dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) involving fractional derivative with Mittag-Leffler kernel

Since 2012, the Middle East has seen a steady rise in the Middle East Respiratory Syndrome Coronavirus (MERS-CoV). A fractional derivative of the non-singular Mittag-Leffler type is used in this research to conduct a mathematical analysis of the dynamics of MERS-CoV infection transmission. The dynamics of such a disease with an additional degree of freedom and non-singular behavior are discovered through the use of the aforementioned fractional operator, and this is one of the important components of our prepared paper. Using the concept of fixed point theory, the existence and uniqueness of solutions are demonstrated. The stability analysis is also tested with the help of the Ulam–Hyers approach, respectively. The numerical solution has been conducted by using the fractional Adams–Bashforth scheme. In the numerical simulation, all classes are demonstrated through the graphical presentation regarding the changing values of fractional-order at time t. The results at various fractional-order laying between (0,1] are drawn with the help of Matlab. We also provide a comparison of the proposed approach with that of the Caputo operator. The outcomes that were achieved illustrate that the considered scheme is highly methodical and very efficient compared to the Caputo fractional operator.

Quasinormal modes, shadow, and greybody factors of 5D electrically charged Bardeen black holes

We study quasinormal modes (QNMs) in 5D electrically charged Bardeen black holes spacetime by considering the scalar and electromagnetic field perturbations. The black holes spacetime is an exact solution of Einstein gravity coupled to nonlinear electrodynamics in five dimensions, which has nonsingular behavior. To calculate QNMs, we use the WKB approximation method up to sixth order. Due to the presence of electric charge $q_e > 0$, both the scalar and electromagnetic field perturbations decay more slowly when compared to the Schwarzschild-Tangherlini black holes. We discover that the scalar field perturbations oscillate more rapidly when compared to the electromagnetic field perturbations. In terms of damping, the scalar field perturbations damp more quickly. Graphically we show that the transmission (reflection) coefficients decrease (increase) with an increase in the magnitude of the electric charge $q_e$. The emission of gravitational waves allows spacetime to undergo damped oscillations due to the nonzero value of the imaginary part, which is always negative. The imaginary part of the QNMs frequencies is continuously decreasing with an increase in the magnitude of the electric charge $q_e$ for a given mode ($l,n$). A connection between the QNMs frequencies and the black hole shadow, as well as the geometric cross-section in the eikonal limit, is also described.

Optical selection rules of zigzag graphene nanoribbons

We present an analytical tight-binding theory of the optical properties of graphene nanoribbons with zigzag edges. Applying the transfer matrix technique to the nearest-neighbor tight-binding Hamiltonian, we derive analytical expressions for electron wave functions and optical transition matrix elements for incident light polarized along the structure axis. It follows from the obtained results that optical selection rules result from the wave function parity factor ${(\ensuremath{-}1)}^{J}$, where $J$ is the band number. These selection rules are that $\mathrm{\ensuremath{\Delta}}J$ is odd for transitions between valence and conduction subbands and that $\mathrm{\ensuremath{\Delta}}J$ is even for transitions between only valence (conduction) subbands. Although these selection rules are different from those in armchair carbon nanotubes, there is a hidden correlation between absorption spectra of the two structures that should allow one to use them interchangeably in some applications. The correlation originates from the fact that van Hove singularities in the tubes are centered between those in the ribbons if the ribbon width is about a half of the tubes circumference. The analysis of the matrix elements dependence on the electron wave vector for narrow ribbons shows a smooth nonsingular behavior at the Dirac points and the points where the bulk states meet the edge states.

Entropic Entanglement: Information Prison Break

We argue that certain nonviolent local quantum field theory (LQFT) modification considered at the global horizon (r=2M) of a static spherically symmetric black hole can lead to adiabatic leakage of quantum information in the form of Hawking particles. The source of the modification is (i) smooth at r=2M and (ii) rapidly vanishing at r≫2M. Furthermore, we restore the unitary evolution by introducing extra quanta which departs slightly from the generic Hawking emission without changing the experience of an infalling observer (no drama). Also, we suggest that a possible interpretation of the Bekenstein-Hawking bound as entanglement entropy may yield a nonsingular dynamical horizon behavior described by black hole thermodynamics. Hence, by treating gravity as a field theory and considering its coupling to the matter fields in the Minkowski vacuum, we derive the conjectured fluctuations of the background geometry of a black hole.

Time scales at quantum phase transitions in the Lipkin-Meshkov-Glick model

We report on quantum revivals and classical periodicities of wave packets centered around the ground state within the Lipkin-Meshkov-Glick model. Special attention is paid to the behavior at first- and second-order phase transitions. In line with previous studies, we find that away from criticality, characteristic times exhibit smooth, nonsingular behavior, but upon approaching the transition points they diverge as power laws with associated critical exponents. Finite-size effects are studied and the observed phenomenology is discussed in the framework of the time-energy uncertainty relation.

Revival times at quantum phase transitions

The concept of quantum revivals is extended to many-body systems and the implications of traversing a quantum phase transition are explored. By analyzing two different models, the vibron model for the bending of polyatomic molecules and the Dicke model for a quantum radiation field interacting with a system of two-level atoms, we show evidence of revival behavior for wave packets centered around energy levels as low as the fundamental state. Away from criticality, revival times exhibit smooth, nonsingular behavior, and are proportional to the system size. Upon approaching a quantum critical point, they diverge as a power law and scale with the system size, although the scaling is no longer linear.

Archimedean-type force in a cosmic dark fluid. I. Exact solutions for the late-time accelerated expansion

We establish a new self-consistent model in order to explain from a unified viewpoint two key features of the cosmological evolution: the inflation in the early Universe and the late-time accelerated expansion. The key element of this new model is the Archimedean-type coupling of the dark matter with dark energy, which form the so-called cosmic dark fluid. We suppose that dark matter particles immersed into the dark energy reservoir are affected by the force proportional to the four-gradient of the dark energy pressure. The Archimedean-type coupling is shown to play a role of effective energy-momentum redistributor between the dark matter and the dark energy components of the dark fluid, thus providing the Universe evolution to be a quasiperiodic and/or multistage process. In the first part of the work we discuss a theoretical base and new exact solutions of the model master equations. Special attention is focused on the exact solutions, for which the scale factor is presented by the anti-Gaussian function: these solutions describe the late-time acceleration and are characterized by a nonsingular behavior in the early Universe. The second part contains qualitative and numerical analysis of the master equations; we focus there on the solutions describing a multi-inflationary Universe.

Archimedean-type force in a cosmic dark fluid. II. Qualitative and numerical study of a multistage universe expansion

In this (second) part of the work we present the results of numerical and qualitative analysis, based on a new model of the Archimedean-type interaction between dark matter and dark energy. The Archimedean-type force is linear in the four-gradient of the dark energy pressure and plays a role of self-regulator of the energy redistribution in a cosmic dark fluid. Because of the Archimedean-type interaction the cosmological evolution is shown to have a multistage character. Depending on the choice of the values of the model guiding parameters,the Universe's expansion is shown to be perpetually accelerated, periodic or quasiperiodic with finite number of deceleration/acceleration epochs. We distinguished the models, which can be definitely characterized by the inflation in the early Universe, by the late-time accelerated expansion and nonsingular behavior in intermediate epochs, and classified them with respect to a number of transition points. Transition points appear, when the acceleration parameter changes the sign, providing the natural partition of the Universe's history into epochs of accelerated and decelerated expansion. The strategy and results of numerical calculations are advocated by the qualitative analysis of the instantaneous phase portraits of the dynamic system associated with the key equation for the dark energy pressure evolution.

Assessment of a simple function to evaluate the relationship between mass flux reduction and mass removal for organic-liquid contaminated source zones

The efficacy of a simple mass-removal function for characterizing mass-flux-reduction/mass-removal behavior for organic-liquid contaminated source zones was evaluated using the data obtained from a series of flow-cell experiments. The standard function, which employs a constant exponent, could not adequately reproduce the non-singular (multi-step) behavior exhibited by the measured data. Allowing the exponent to change as a function of mass removal (as the organic-liquid distribution and relative permeability change) produced non-singular relationships similar to those exhibited by the measured data. Four methods were developed to dynamically inform the exponent through use of measurable system-indicator parameters. Key factors that mediate the magnitude of mass flux (dilution and source accessibility) were accounted for using measures of source zone cross-sectional area, ganglia-to-pool (GTP) ratio, and relative permeability. The two methods that incorporated only the ganglia-to-pool ratio produced adequate simulations of the observed behavior for early stages of mass removal, but not for later stages. The method that incorporated parameters accounting for the source zone cross-sectional area (i.e., measure of system dilution) and source accessibility (GTP ratio and relative permeability) provided the most representative simulations of the observed data.

Born–Infeld determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

In the context of Born–Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.

KINEMATICS OF FLOWS ON CURVED, DEFORMABLE MEDIA

Kinematics of geodesic flows on specific, two-dimensional, curved surfaces (the sphere, hyperbolic space and the torus) are investigated by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation, for a variety of initial conditions. For flows on the sphere and on hyperbolic space, we show the existence of singular (within a finite value of the time parameter) as well as non-singular solutions. We illustrate our results through a phase diagram which demonstrates under which initial conditions (or combinations thereof) we end up with a singularity in the congruence and when, if at all, we can obtain non-singular solutions for the kinematic variables. Our analysis portrays the differences which arise due to positive or negative curvature and also explores the role of rotation in controlling singular behavior. Subsequently, we move on to geodesic flows on two-dimensional spaces with varying curvature. As an example, we discuss flows on a torus. Characteristic oscillatory features, dependent on the ratio of the two radii of the torus, emerge in the solutions for the expansion, shear and rotation. Singular (within a finite time) and non-singular behavior of the solutions are also discussed. Finally, we conclude with a generalization to three-dimensional spaces of constant curvature, a summary of some of the generic features obtained and a comparison of our results with those for flows in flat space.

Probing the Geometry of Warped String Compactifications at the Large Hadron Collider

Warped string compactifications, characterized by the nonsingular behavior of the metric in the infrared (IR), feature departures from the usual anti-de Sitter warped extra dimensions. We study the implications of the smooth IR cutoff for Randall-Sundrum- (RS-)type models. We find that the phenomenology of the Kaluza-Klein gravitons (including their masses and couplings) depends sensitively on the precise shape of the warp factor in the IR. In particular, we analyze the warped deformed conifold, find that the spectrum differs significantly from that of RS, and present a simple prescription (a mass-gap ansatz) that can be used to study the phenomenology of IR modifications to 5D warped extra dimensions.

Mapping from a fragile glass-forming system to a simpler one near their glass transitions

Extensive molecular-dynamics simulations on two different glass-forming systems are performed to test the prediction proposed recently by the mean-field theory (MFT) of glass transition that a fragile system can be mimicked by a simpler one near their glass transitions. One is a simulation for a hard-sphere fluid with size polydispersity where the volume fraction φ is a control parameter and the other is for a Lennard-Jones binary mixture where the inverse temperature 1 / T is a control parameter. Then, their mean-square displacements are fully analyzed by MFT. Thus, we show that both results are collapsed on a master curve given by MFT when D S L ( φ ) = D S L ( T ) , where D S L is a long-time self-diffusion coefficient. We also investigate the non-singular behavior of D S L consistently from a unified standpoint based on MFT. Thus, we show that macroscopic physical quantities in a fragile system can be transformed into those in a simpler one through a universal parameter D S L .

THE SCHWARZSCHILD SOLUTION IN THE DGP MODEL

We discuss the Schwarzschild solution in the Dvali–Gabadadze–Porrati (DGP) model. We obtain a perturbative expansion and find the explicit form of the lowest-order contribution. By keeping off-diagonal terms in the metric, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the perturbative expansion yields the standard four-dimensional Schwarzschild solution on the brane which is non-singular in the decoupling limit. This non-singular behavior is similar to the Vainshtein solution in massive gravity demonstrating the absence of the van Dam–Veltman–Zakharov (vDVZ) discontinuity in the DGP model.

Nonsingular FRW cosmology and nonlinear electrodynamics

The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat Friedmann-Robertson-Walker (FRW) geometry we derive the general nonsingular solution supported by a magnetic field plus a cosmic fluid and a nonvanishing vacuum energy density. The nonsingular behavior of solutions with a time-dependent $\ensuremath{\Lambda}(t)$ term are also examined. As a general result, it is found that the functional dependence of $\ensuremath{\Lambda}(t)$ can uniquely be determined only if the magnetic field remains constant. All these models are examples of bouncing universes which may exhibit an inflationary dynamics driven by the nonlinear corrections of the magnetic field.

リング状震源による衝撃応答(S13-2 動的問題,S13 数理弾性力学応用の最前線)

An exact Green's function for radially symmetric waves in a cylindrically anisotropic and inhomogeneous solid is presented. Non-singular behavior at the front of focused wave is found and is anisotropy and inhomogeneity parameters determine the behavior. Time-harmonic Green's function in the case of linear velocity variation shows non-wave nature at lower frequency than a critical one that is also defined by material parameters.

Critical behavior of thermal parameters at the smectic-A-hexatic-B and smectic-A-smectic-C phase transitions in liquid crystals.

High temperature resolution measurements of thermal conductivity, thermal diffusivity, and specific heat, with simultaneous polarized light visual inspection of the sample, have been performed at two different liquid crystal phase transitions: the SmA-SmC (Smectic-A-Smectic-C) and the SmA-HexB (Smectic-A-hexatic-B) in racemic A7 [4-(3-methyl-2-chlorobutanoyloxy)-4(')-heptyloxybiphenyl] and 65OBC (n-hexyl-4(')-n-pentyloxybiphenyl-4-carboxylate) compounds, respectively. In the past, anomalies in the thermal conductivity at the transitions have been reported. Our results indicate a nonsingular behavior of the thermal conductivity at both transitions, similarly to what has been previously reported for the smectic-A-nematic phase transition. It is also shown how, in several cases, the nature of the transition can be affected by the sample thermal history due to the presence of strain annealing phenomena.

Thermodynamic Compressibility Measurements in the Context of 2D Metal–Insulator Transition

Presented in this work is a comparative study of the thermodynamic compressibility of two different two dimensional systems in GaAs/AlGaAs heterostructures. In the two-dimensional hole system, electron–electron interactions are strong and possibly the reason for an anomalous temperature dependence in the resistivity that is reminiscent of metallic behavior which is known not to exist in a non-interacting two dimensional Fermi gas. The other system is a two-dimensional electron system where interactions are much weaker and whose transport properties have been understood in the context of scaling theory. The thermodynamic compressibility of both systems are measured. An unequivocal signature for a phase transition is found in the compressibility measurements for the hole system. In contrast, a very different, non-singular behavior is observed in the electron system. The experimental results are compared with a recent theoretical work.

Diffuse interface analysis of crystal nucleation in hard-sphere liquid

We show that the increase of the interface free energy with deviation from equilibrium seen in recent Monte Carlo simulations [S. Auer and D. Frenkel, Nature (London) 413, 711 (2001)] can be recovered if the molecular scale diffuseness of the crystal–liquid interface is considered. We compare two models, Gránásy’s phenomenological diffuse interface theory, and a density functional theory that relies on the type of Ginzburg–Landau expansion for fcc nucleation, that Shih et al. introduced for bcc crystal. It is shown that, in the range of Monte Carlo simulations, the nucleation rate of the stable fcc phase is by several orders of magnitude higher than for the metastable bcc phase, seen to nucleate first in other fcc systems. The nucleation barrier that the diffuse interface theories predict for small deviations from equilibrium is in far better agreement with the simulations than the classical droplet model. The behavior expected at high densities is model dependent. Gránásy’s phenomenological diffuse interface theory indicates a spinodal point close to glass transition, while a nonsingular behavior is predicted by the density functional theory with constant Ginzburg–Landau coefficients. Remarkably, a minimum of the nucleation barrier, similar to the one seen in polydisperse systems, occurs if the known density dependence of the Ginzburg–Landau coefficients is considered.

Nonsingular behavior near the colloidal glass transition

A heuristic hypothesis is given for the colloidal glass transition on the basis of the theoretical analyses of experimental data from a unified viewpoint obtained recently by the present author. Three regions, a liquid region, a supercooled liquid region, and a glass region, are distinguished. No divergence of the α- and β-relaxation times is found at the glass transition, although the kinetic and thermodynamic-like properties of the colloidal liquid exhibit drastic changes in the supercooled region.