Related papers: On the Velocity Tensors
It is shown that conventional "covariant" derivative of the Levi-Civita tensor is not really covariant. Adding compensative terms, it is possible to make it covariant and to be equal to zero. Then one can be introduced a curvature in the…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative velocity is discussed. The notions of deformation velocity tensor, shear…
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…
A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…
To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor $Q=\exp W$.
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical…
A vector-tensor theory of gravity that was introduced in an earlier publication is analyzed in detail and its consequences for early universe cosmology are examined. The multiple light cone structure of the theory generates different speeds…
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
A new vector-tensor model of classical gravity, which contains coupling between the field strength of the vector field and the curvature tensors in six dimensions, is proposed. Cosmological solutions of the scale factors in this model with…
The reciprocal velocity force, $F(v)=\frac{C}{v}$, despite its theoretical and practical importance, is often neglected in mechanics courses. We use graphical methods to explain how such a force naturally arises from a device called a…
Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials updates. The…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
A rigid object of general shape is fixed inside a wind tunnel. The drag force exerted on it by the wind is determined by a new method based on simple basic Physics concepts, provided one has a solver, any solver, for the corresponding…
General relativity is the theory with unclear energy momentum tensor. An approach is considered, allowing to construct the energy momentum tensor for relativity with nonsymmetric metric. A consequence of the approach is confirmed in the…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two important quantities, whose positivity is a necessary and…
We study geometric properties of a random Gaussian short-time correlated velocity field by considering statistics of a passively advected metric tensor. That describes universal properties of fluctuations of tensor objects frozen into the…