We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. The model is derivable from a continuous-time Boltzmann-BGK equation in the presence of an intercomponent...

We calculate all planar contributions to the two-loop massless helicity amplitudes for process $q\bar q\to \gamma\gamma\gamma$. The results are presented in fully analytic form terms of functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide already used us NNLO QCD calculation LHC $pp\to \gamma\gamma\gamma$ [Chawdhry et al. (2019)]. Our agree with a recen...

This work addresses the Prime Geodesic Theorem for Picard manifold $\mathcal{M} = \mathrm{PSL}_{2}(\mathbb{Z}[i]) \backslash \mathfrak{h}^{3}$, which asks asymptotic evaluation of a counting function closed geodesics on $\mathcal{M}$. Let $E_{\Gamma}(X)$ be error term in Theorem. We establish that $E_{\Gamma}(X) O_{\varepsilon}(X^{3/2+\varepsilon})$ average as well many pointwise bounds. The se...

We consider in this note one-side Liouville properties for viscosity solutions of various fully nonlinear uniformly elliptic inequalities, whose prototype is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F left-parenthesis x comma upper D squared u right-parenthesis greater-than-or-equal-to H Subscript i Baseline right-parent...

We discuss the amplitude of $B\to l^+l^-l'\nu'$ decays and differential decay rate $d^2\Gamma/dq^2dq'^2$, $q$ momentum $l^+l^-$ pair emitted from electromagnetic vertex $q'$ $l'\nu'$ weak vertex. For relevant form factors, we construct dispersion representations in $q^2$ which consistently take into account Ward identity constraints at $q^2=0$ contributions light vector resonances. This allows ...

The aim of this paper is to construct generating functions for q-beta polynomials. By using these generating functions, we define the q -beta polynomials and also derive some fundamental properties of these polynomials. We give some functional equations and partial differential equations (PDEs) related to these generating functions. By using these equations, we find some identities related to t...

In the present paper, we study Cauchy-Dirichlet problem to a nonlocal nonlinear diffusion equation with polynomial nonlinearities $$\mathcal {D}_{0|t}^{\alpha }u+(-\varDelta )^s_pu=\gamma |u|^{m-1}u+\mu |u|^{q-2}u,\,\gamma ,\mu \in \mathbb {R},\,m>0,q>1,$$ involving time-fractional Caputo derivative }$$ and space-fractional p-Laplacian operator $$(-\varDelta )^s_p$$ . We give simple proof of co...