We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using ...

Hydraulic fracturing is a procedure by which a fracture is initiated and propagates due to pressure (hydraulic loading) applied by a fluid introduced inside the fracture. In this study we focus on a crack driven by an ...

Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, ...

© 2018 authors. Published by the American Physical Society. Starting from solutions of the lightly bound Skyrme model, we construct many new Skyrmion solutions of the standard Skyrme model with tetrahedral or octahedral ...

Spiral density waves dominate several facets of accretion disc dynamics – planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, ...

© 2018 authors. We present results of a lattice QCD calculation of B→D∗ and Bs→Ds∗ axial vector matrix elements with both states at rest. These zero recoil matrix elements provide the normalization necessary to infer a ...

The high-frequency quasi-periodic oscillations (HFQPOs) that punctuate the light curves of X-ray binary systems present a window onto the intrinsic properties of stellar-mass black holes and hence a testbed for general ...

This paper considers the interaction of turbulence with a serrated leading edge. We investigate the noise produced by an aerofoil moving through a turbulent perturbation to uniform flow by considering the scattered pressure ...

An iterated marching method is presented for reconstruction of rough perfectly reflecting 1-dimensional surfaces from scattered data arising from a scalar wave at grazing incidence. This is based on coupled inte- gral ...

The physics of the dark energy and the dark matter is still an open issue in cosmology. The dark energy occupies about 68.5% of the total energy density of the universe today [1], and is believed to accelerate its observed ...

We use two-dimensional direct numerical simulations of Boussinesq stratified shear layers to investigate the influence of the minimum gradient Richardson number Rim on the early time evolution of Kelvin–Helmholtz instability ...

We describe non-relativistic limits of the 3D Proca and $\sqrt{\rm Proca}$ theories that yield spin-1 Schroedinger equations. Analogous results are found by generalized null reduction of the 4D Maxwell or complex self-dual ...

We consider the self-induced motions of three-dimensional oblate spheroids of density $\rho_s$ with varying aspect ratios $AR=b/c \leq 1$, where $b$ and $c$ are the spheroids' centre-pole radius and centre-equator radius ...

We study inflation in models with many interacting fields subject to randomly generated scalar potentials. We use methods from non-equilibrium random matrix theory to construct the potentials and an adaption of the ‘transport ...

How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently developed energy optimization method for identifying the minimal disturbance ...

We consider the steady, supercritical flow of a fluid layer. The layer is bounded above by a free surface and below by a rigid no-slip base. The base is in two parts: the downstream part of the base is stationary, while ...

In the context of f(R)-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f(R) ...

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D=4,5,7, which linearises invariance under the AdS isometry group Sp(4;K) for K=R,C,H,, is generalized to the massless N-extended ...

Is the future predictable? If we know the initial state of a system exactly, then do the laws of physics determine its state arbitrarily far into the future? In Newtonian mechanics, the answer is yes. Similarly in ...

The positive semidefinite rank of a convex body $C$ is the size of its smallest positive semidefinite formulation. We show that the positive semidefinite rank of any convex body $C$ is at least $\sqrt{\log d}$ where $d$ is ...