The standard mass action, which assumes that infectious disease transmission occurs in well‐mixed populations, is popular for formulating compartmental epidemic models. Compartmental epidemic models ...often follow standard mass action for simplicity and to gain insight into transmission dynamics as it often performs well at reproducing disease dynamics in large populations. In this work, we formulate discrete time stochastic susceptible‐infected‐removed models with linear (standard) and nonlinear mass action structures to mimic varying mixing levels. Using simulations and real epidemic data, we demonstrate the sensitivity of the basic reproduction number to these mathematical structures of the force of infection. Our results suggest the need to consider nonlinear mass action in order to generate more accurate estimates of the basic reproduction number although its uncertainty increases due to the addition of one growth scaling parameter.
•The dot product of generalized flux and force is used to construct the least action principle.•The action of heat conduction is the entransy dissipation rather than the entropy production.•A least ...generalized entransy dissipation principle for nonlinear heat conduction is introduced.•The least entransy dissipation principle is applied to optimize a heat conduction problem.
The least action principle is used in various disciplines including linear transport processes. However, non-equilibrium thermodynamic analyses of linear transport processes involve the dot product of the thermodynamic flux and the thermodynamic force which must be the entropy production rate in the linear phenomenological law for such processes; thus, Fourier’s heat conduction law cannot be derived based on the variation of the entropy production rate. A generalized linear phenomenological law for various types of linear transport processes, including heat conduction, mass diffusion, electric conduction and fluid flow in porous medium is introduced here where the dot product of a generalized flux and a generalized force is taken as the action to give the generalized linear phenomenological law. For heat conduction, the entransy dissipation rate, which is the dot product of the heat flux and the negative of the temperature gradient, is taken as the action, and the variation of the entransy dissipation rate then leads to Fourier’s heat conduction law with constant thermal conductivity. Hence, the action of heat conduction process is the entransy dissipation rate rather than the entropy production rate. A nonlinear constitutive relation for the heat conduction with temperature dependent thermal conductivity is then converted to a linear problem by introducing a generalized temperature, which gives a least generalized entransy dissipation principle for nonlinear heat conduction processes. Finally, the least entransy dissipation principle is applied to optimize a one-dimensional heat conduction problem without heat-work conversion as an example where the minimum entropy generation principle is not applicable.
Irreversibility (that is, the “one-sidedness” of time) of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy ...and its production rate have been generally regarded as Lyapunov functions in order to measure the irreversibility of various physical processes. In fact, the Lyapunov function is not always unique. In the represent work, a rigorous proof is given that the entransy and its dissipation rate can also serve as Lyapunov functions associated with the irreversibility of the heat conduction process without the conversion between heat and work. In addition, the variation of the entransy dissipation rate can lead to Fourier’s heat conduction law, while the entropy production rate cannot. This shows that the entransy dissipation rate, rather than the entropy production rate, is the unique action for the heat conduction process, and can be used to establish the finite element method for the approximate solution of heat conduction problems and the optimization of heat transfer processes.
We present two results on the analysis of discrete dynamical systems and finite difference discretizations of continuous dynamical systems, which preserve their dynamics and essential properties. The ...first result provides a sufficient condition for forward invariance of a set under discrete dynamical systems of specific type, namely time-reversible ones. The condition involves only the boundary of the set. It is a discrete analog of the widely used tangent condition for continuous systems (
viz.
the vector field points either inwards or is tangent to the boundary of the set). The second result is nonstandard finite difference (NSFD) scheme for dynamical systems defined by systems of ordinary differential equations. The NSFD scheme preserves the hyperbolic equilibria of the continuous system as well as their stability. Further, the scheme is time reversible and, through the first result, inherits from the continuous model the forward invariance of the domain. We show that the scheme is of second order, thereby solving a pending problem on the construction of higher-order nonstandard schemes without spurious solutions. It is shown that the new scheme applies directly for mass action-based models of biological and chemical processes. The application of these results, including some numerical simulations for invariant sets, is exemplified on a general Susceptible-Infective-Recovered/Removed (SIR)-type epidemiological model, which may have arbitrary large number of infective or recovered/removed compartments.
This paper is dedicated to studying the existence of periodic solutions to a new class of forced damped vibration systems by the variational method. The advantage of this kind of system is that the ...coefficient of its second order term is a symmetric $N \times N$ matrix valued function rather than the identity matrix previously studied. The variational principle of this problem is obtained by using two methods: the direct method of the calculus of variations and the semi-inverse method. New existence conditions of periodic solutions are created through several auxiliary functions so that two existence theorems of periodic solutions of the forced damped vibration systems are obtained by using the least action principle and the saddle point theorem in the critical point theory. Our results improve and extend many previously known results.
The linearized version of a recently formulated Variational Macroscopic Theory of biphasic isotropic Porous Media (VMTPM) is employed to derive a general stress partitioning law for media undergoing ...flow conditions under prevented fluid seepage and negligible inertia effects, typically met in biphasic specimens subjected to jacketed tests.
The principle of virtual work, relevant to the specialization of VMTPM to such characteristic flow conditions, naturally yields a stress partitioning law, between solid and fluid phase of a saturated medium, that exactly matches with the celebrated Terzaghi’s principle. It is also shown that the stress tensor of the solid phase work-associated with the strain measure of the VMTPM naturally corresponds to the Terzaghi’s effective stress. Accordingly, under undrained conditions, Terzaghi’s law is proved to be a completely general stress partitioning law for a saturated biphasic medium irrespective of its constitutive and/or microstructural features as well as of the compressibility of its constituent phases.
Since the developments reported are obtained ruling out thermodynamic constraints and any assumption on the internal microstructure and on the compressibility of the phases, the results obtained indicate that Terzaghi’s law could more generally apply to a broader class of biphasic media and be not restricted within the context of geomechanics.
We consider gravity in four dimensions in the vielbein formulation, where the fundamental variables are a tetrad
e
and a SO(3,1) connection
ω
. We start with the most general action principle ...compatible with diffeomorphism invariance which includes, besides the standard Palatini term, other terms that either do not change the equations of motion, or are topological in nature. For our analysis we employ the covariant Hamiltonian formalism where the phase space
Γ
is given by solutions to the equations of motion. We consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. For this extended action we study the effect of the topological terms on the Hamiltonian formulation. We prove two results. The first one is rather generic, applicable to any field theory with boundaries: The addition of topological terms (and any other boundary term) does not modify the symplectic structure of the theory. The second result pertains to the conserved Hamiltonian and Noether charges, whose properties we analyze in detail, including their relationship. While the Hamiltonian charges are unaffected by the addition of topological and boundary terms, we show in detail that the Noether charges
do
change. Thus, a non-trivial relation between these two sets of charges arises when the boundary and topological terms needed for a consistent formulation are included.
•Stress in an elastic thin plate subjected to surface forces distributes non-uniformly due to Saint-Venant’s principle.•Thus, the light intensity transmitted through an electro-stress birefringence ...should be different point by point.•Based on this, the measurement of two-dimension micro-displacement can be realized with the electro-birefringence bilayer.
A bilayer composite with electro-birefringence effect was fabricated using ferroelectric and stress-birefringence medium. Its electro-optical response was studied. The transmission light intensity was found to change with displacement of the incident beam to the elastic-optical layer in two dimensions perpendicular to the beam. The effects of local-action and interfacial elastic coupling on the stress distribution in the elastic-optical material were analyzed. Starting from the basic equations of elasticity, a physical model of electro-stress birefringence for the bilayer composite was derived. It was found that the theoretical calculations in general accord with the experimental results without considering ferroelectric relaxation. And the micro-displacement sensing of two-dimension was realized with the bilayer composite of electro-stress birefringence.
On the basis of a general action principle, we revisit the scale invariant field equation using the cotensor relations by Dirac (1973). This action principle also leads to an expression for the scale ...factor λ, which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler’s third law is a remarkable scale-invariant property.
PDF
