An assessment of five different definitions of the principal molecular axis along which molecules align in a nematic liquid crystal system has been made by analysing fully atomistic molecular dynamics (MD) simulations of a set of anthraquinone dyes in the cyanobiphenyl-based nematic host mixture E7. Principal molecular axes of the dyes defined by minimum moment of inertia, minimum circumference...

We present Variable Eddington Tensor-closed Transport on Adaptive Meshes (\texttt{VETTAM}), a new algorithm to solve the equations of radiation hydrodynamics (RHD) with support for adaptive mesh refinement (AMR) in frequency-integrated, two-moment formulation. The method is based non-local Tensor (VET) closure computed hybrid characteristics scheme ray tracing. use Godunov hyperbolic transport ...

In this article, we introduce nonlinear versions of the popular structure tensor, also known as second moment matrix. These nonlinear structure tensors replace the Gaussian smoothing of the classical structure tensor by discontinuity-preserving nonlinear diffusions. While nonlinear diffusion is a well-established tool for scalar and vector-valued data, it has not often been used for tensor imag...

We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix. Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation’s amplitude, deterministic equations for k moments of the random solution. The solution’s k-th moment satisfies a k-fold tensor product boundary value problem on the k-fold pr...

Numerical methods for stochastic ordinary differential equations typically estimate moments of the solution from sampled paths. Instead, in this paper we directly target the deterministic equation satisfied by the first and second moments. For the canonical examples with additive noise (Ornstein–Uhlenbeck process) or multiplicative noise (geometric Brownian motion) we derive these deterministic...

New bounds are derived on the e ective heat conductivity tensor for an anisotropic two-phase composite with interfacial surface resistance between phases. The new upper bound is given in terms of the two-point correlation function, component volume fractions and moment of inertia tensor for the surface of each heterogeneity. The new lower bound is given in terms of the interfacial surface area,...

In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of four-velocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are deri...

We have developed a method that inverts seismic body waves to determine the mechanism and rupture pattern of earthquakes. The rupture pattern is represented as a sequence of subevents distributed on the fault plane. This method is an extension of our earlier method in which the subevent mechanisms were fixed, in the new method, the subevent mechanisms are determined from the data and are allowe...

We define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals...