Related papers: Third order quasi-compact schemes for space temper…
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation…
In this paper, we introduce a complete family of parametrized quasi-probability distributions in phase space and their corresponding Weyl quantization maps with the aim to generalize the recently developed Wigner-Weyl formalism within the…
The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of…
Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they…
The one loop matching kernels between parton distribution functions (PDFs) for parton $i=u,d,s,g$ and their corresponding quasi-PDFs are computed at one loop in the hybrid-ratio scheme. We found that, in addition to the conservation of the…
Compressive isothermal turbulence is known to have a near lognormal density probability distribution function (PDF) with a width that scales with the sonic Mach number and nature of the turbulent driving (solenoidal vs compressive).…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We discuss the current developments by the European Twisted Mass Collaboration in extracting parton distribution functions from the quasi-PDF approach. We concentrate on the non-perturbative renormalization prescription recently developed…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
The pair-interactions U_{ij}(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., g_{ij}(r). Great simplicity is achieved if U_{ij}(r) could be directly used to predict…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…
The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy…
Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result…
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
We derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) correlator, including kinematic power corrections to all orders. The resulting expression involves only twist-two TMD distributions and is frame…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…