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The $q$-theory approach to the cosmological constant problem is reconsidered. The new observation is that the effective classical $q$-theory gets modified due to the backreaction of quantum-mechanical particle production by spacetime…
We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is…
A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with…
This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…
Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is $1/2$. There then exist lean and rich premixed flames of roughly equal…
Conjugate heat transfer is a challenging fluid-structure coupling problem that can significantly influence flame stabilization and thermoacoustic instabilities. To properly capture combustion phenomena that involve conjugate heat transfer,…
Thin flame dynamics in a turbulent flow remains debated, with various parameterizations proposed for the typical flame propagation velocity. According to the classical Damk\"ohler's model based on Huygens' principle, a flame front should…
We use general concepts of statistical mechanics to compute the quantum frictional force on an atom moving at constant velocity above a planar surface. We derive the zero-temperature frictional force using a non-equilibrium…
We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange…
In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…
This paper studies the dynamical behavior near a new family of explicit self-similar solutions for the one dimensional Born-Infeld equation. This quasilinear scalar field equation arises from nonlinear electromagnetism, as well as branes in…
A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy…
The traditional Standard Quantum Mechanics (SQM) theory is unable to solve the Spin-s problem, i.e., to justify the utterly important "Pauli Exclusion Principle". A complete and straightforward solution of the Spin-Statistics problem is…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these…
A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent…