Using the principle of energy conservation and laws of geometrical optics, we derive the photon transport equation for turbid biological media with spatially varying isotropic refractive index. We show that when the refractive index is constant, our result reduces to the standard radiative transfer equation and when the medium is lossless and free of scattering to the well known geometrical opt...

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength[1, 2]. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics[3], which is founded on the principle of conservation of energy, provide...

We prove that the Cohesiveness Principle (COH ) is Π1 conservative over RCA0 + IΣn and over RCA0 + BΣn for all n ≥ 2. (The cases for n ≥ 3 are new.) Our approach is recursiontheoretic. We first characterize COH over RCA0 +BΣ2 as a ‘jumped’ version of Weak König’s Lemma (WKL) and develop suitable machinery including a version of the Friedberg jumpinversion theorem. Our main theorem is obtained w...

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. We therefore investigate a sec...

Aquasi-incompressible hydrodynamic phase fieldmodel for flows of fluidmixtures of two incompressible viscous fluids of distinct densities and viscosities is derived by using the generalized Onsager principle, which warrants the variational structure, the mass conservation and energy dissipation law. We recast the model in an equivalent form and discretize the equivalent system in space firstly ...

A model with flat FRW symmetries and G and Λ, variable is considered in such a way that the momentum-energy tensor that describes the model is characterized by a bulk viscosity parameter. For this tensor the conservation principle is taken into account. In this paper it is showed how to apply the dimensional method in order to solve the outlined equations in a trivial way. Keywords— Odes, AD, F...

Modeling and simulation of processing plants are widely used in industry. Construction of a mathematical model for a plant is a time-consuming and error-prone task. In light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. Many software tools for modeling, simulation and optimization of proces...

In a matching paper [16], I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique alphabet. This was substantiated to a very high level of significance using some 55 million lines of source code of mixed provenance. The principle was also applied to show...

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B(m) = m, the specific value of the exponent p is the object of an ongoing debate, with many mecha...

Equations related with wave propagation are reexamined as in certain circumstances law of conservation of energy is not fulfilled even though it is cautiously clarified with the help of Heisenberg’s uncertainty principle. Recently, attempt has also been made to understand certain discrepancies in optical phenomena like diffraction or interference. The purpose of the present investigation, there...