A second-sound based, hyperbolic SIR model for high-diffusivity spread

We present an analytical study of one-dimensional (1D) kinematic wave phenomena under a hyperbolic SIR model based not on Fick's diffusion law, but rather on the inertial-type II flux law of second-sound theory. Unlike in the Ficken context, we are able to derive exact traveling wave solutions (TWS)s, as well as explicit asymptotic/approximate expressions, for both the susceptibles and infectives. We also determine, using singular surface theory, how shock-fronts resulting from initial jump discontinuities propagate and evolve under this model. In particular, critical values and special cases are examined and possible mitigation methods, which take the form of parameter-value manipulation(s), are noted.     

Vibration of simply supported cylindrical shells with longitudinal stiffeners

The vibration of simply supported cylindrical shells stiffened by discrete longitudinal stiffeners is investigated by using an energy method. Vlasov's thin walled beam theory is used for stringers. Shell theories based on Donnell's approximate theory and Flügge's more exact theory are used for the skin and numerical results indicate that Donnell's approximate theory gives excellent results for the stiffened shells. Sinusoidal wave form is considered in the longitudinal direction, and mode shapes in the circumferential direction are represented by Fourier series. Numerical results on frequencies and mode shapes computed for a shell stiffened by various number of stiffeners are presented and compared favorably with existing experimental results and other analytical solutions.     

Stochastic Perturbation of Power Law Optical Solitons

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons, with power law nonlinearity, in addition to deterministic perturbations, that is governed by the nonlinear Schrödinger’s equation. The Langevin equations are derived and analysed. The deterministic perturbations that are considered here are due to filters and nonlinear damping.     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.     

Statistical Dynamics of Solitons in Optical Fibers

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons in addition to deterministic perturbations of optical solitons that are governed by the nonlinear Schro¨dinger's equation. The Langevin equations are derived and analyzed. The deterministic perturbations that are considered here are of both Hamiltonian as well as of non-Hamiltonian type.     

Stochastic perturbation of Kerr law optical solitons

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons, due to Kerr law nonlinearity, in addition to deterministic perturbations of optical solitons that is governed by the nonlinear Schrödingers equation. The Langevin equations are derived and analyzed. The deterministic perturbations that are considered here are of both Hamiltonian as well as of non-Hamiltonian type.     

Variational Formulation of Approximate Symmetries and Conservation Laws

We show how the conserved vectors and associated (approximate) Lie symmetry generators of a partial differential equation with a small parameter can be utilized to construct approximate Lagrangians for the equation. We then use the Lagrangian to further determine approximate Noether symmetries and, hence, new associated conservation laws. The theory is applied to a number of perturbations of the wave equation.     

The variational and virial-like theory of oscillations and stability of non-conservative and/or non-linear mechanical systems

This paper presents the general theory and some applications of Hamiltonian action and virial-like methods to the exact and/or approximate study of the periodic solutions of non-conservative and/or non-linear, but holonomic, oscillators. Specifically, the first (theoretical) part covers: (i) a generalization of “Hamilton's law of varying action”, to include variable time-endpoints (i.e., frequency variations) and variable system parameters, such as elasticity and/or inertia, and (ii) a general formulation of the “virial” theorem and its use in determining the stability/instability of given oscillatory motions. Applications of the above (of the Rayleigh-Ritz type) to the following systems are then presented: (i) linear circulatory; (ii) linear conservative, loading parameter dependent, (iii) Duffing's (cubic) oscillator; (iv) van der Pol's oscillator, and related general non-linear and non-conservative case. Comparison of the method with other existing ones, and related open problems (such as limit-cycle stability), are finally discussed.     

Die Strahlungs-Temperatur bewegter Körper

The Radiation Temperature of Moving Bodies The comparison of the temperatures of two bodies which are in a relative motion is possible by the black-body-radiation of these bodies, unambiguously. Then, Planck's transformation law for the temperature is resulting by Einstein's theory of the transversal Doppler-effect and the aberration and by the laws of heat radiation without additional hypotheses. - Our argument is based on the transformation formulas of the specific radiation intensities which are proved by M. v. Laue (1943) in his relativistic deduction of Wien's law.     

The energy tensor of matter in the projectve theory of relativity

In the projective theory of relativity the 5-dimensional field equation \(_{\mu \nu } \) and the resulting equation of motion Tμυ_;μ = 0 are investigated. There Tμυ stands for the 5-dimensional tensor of macroscopic matter. The 4-dimensional field equations and equation of motion obtained by projection are a generalization of Einstein's theory of general relativity and Maxwell's electrodynamics, involving a scalar field φ.They contain a single constant φ₀.The weak field approximation is investigated for the case of an ideal fluid and leads to Newton's mechanics, including Newton's gravitational law, and to Maxwell's electrodynamics. For the constant φ₀ one obtains the approximate value φ₀c⁴/γ_N with Newton's gravitational constant γ_N.For homogeneous and isotropic cosmological models consisting of matter only the general solution for the radius K of curvature is given. This solution is independent of the equation of state of matter For a pure dust universe the general solution for the scalar field φ is given. For a closed universe a power law φ ?K^?1 is valid which leads to Mach's principle. The calculation of the age of a closed universe yields over 7×10⁹y,if one uses mean values of the present cosmological data.     

Causality in the Fermi problem and the Magnus expansion

In 1932, Fermi presented a two-atom model for determining whether quantum mechanics is consistent with causality, and concluded that indeed it is. In the late 1960's, Shirokov and others found that Fermi's approximations may not have been sound, and when corrected, Fermi's model shows non-causal behavior. We show that if instead of time-dependent perturbation theory, the Magnus expansion is used to approximate the time-evolution operator, causality does follow.     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

A new look at Hamilton's principle

Hamilton's principle and Hamilton's law are discussed. Hamilton's law is then applied to achieve direct solutions to time-dependent, nonconservative, initial value problems without the use of the theory of differential or integral equations. A major question has always plagued competent investigators who use “energy methods,” viz., “Why is it that one can derive the differential equations for a system from Hamilton's principle and then solve these equations (at least in principle) subject to applicable initial and boundary conditions; but one cannot obtain a solution directly from Hamilton's principle except in very special cases?” This paper provides the answer to that question. In Hamilton's own words, “... the peculiar combination it [i.e., Hamilton's law] involves, of the principles of variations with those of partial differentials, for the determination and use of an important class of integrals, may constitute, when it shall be matured by the future labors of mathematicians, a separate branch of analysis.”     

Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations

In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge–Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency–amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.     

Intra-channel collision of parabolic law optical solitons

The intra-channel collision of optical solitons, with parabolic law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers along with filters. The suppression of soliton–soliton interaction, in presence of these perturbations terms, is achieved. The numerical simulations support the quasi-particle theory.     

Some exact identities connecting one- and two-particle Green's functions in spin–orbit coupling systems

Some exact identities connecting one- and two-particle Green's functions in the presence of spin–orbit coupling have been derived. These identities are similar to the Ward identity in usual quantum transport theory of electrons. A satisfying approximate calculation of the spin transport in spin–orbit coupling system should also preserve these identities, just as the Ward identities should be remained in the usual electronic transport theory.     

Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the critical circumferential mode number and the minimum flutter load is investigated. As expected, the flutter load increases as the follower force changes from the so-called Beck's load into the so-called Leipholz's and Hauger's loadings. The increased flutter load was calculated for homogeneous shell with different mechanical properties, and it was found that the difference in elasticity moduli bears the most significant effect on the flutter load increase in short, thick shells. Also, for an FGM shell, the increase in the flutter load was calculated directly, and it was found that it can be derived from the simple power law when the corresponding increase for the two base phases are known.