On Theories of Elasto-Plastic Shells in Mixed Tensor Formulation

1986 ◽  
pp. 487-504
Author(s):  
W. Wunderlich ◽  
H. Springer
Keyword(s):  
Tensor Formulation

scholarly journals Multi-Domain Communication Systems and Networks: A Tensor-Based Approach

Network ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 50-74
Author(s):  
Divyanshu Pandey ◽  
Adithya Venugopal ◽  
Harry Leib
Keyword(s):  
Communication Systems ◽  
Physical Layer ◽  
Mathematical Framework ◽  
Trade Off ◽  
Information Theoretic ◽  
Time Frequency ◽  
Tensor Formulation ◽  
Processing Techniques ◽  
Multiple Domains ◽  
Signal Processing Techniques

Most modern communication systems, such as those intended for deployment in IoT applications or 5G and beyond networks, utilize multiple domains for transmission and reception at the physical layer. Depending on the application, these domains can include space, time, frequency, users, code sequences, and transmission media, to name a few. As such, the design criteria of future communication systems must be cognizant of the opportunities and the challenges that exist in exploiting the multi-domain nature of the signals and systems involved for information transmission. Focussing on the Physical Layer, this paper presents a novel mathematical framework using tensors, to represent, design, and analyze multi-domain systems. Various domains can be integrated into the transceiver design scheme using tensors. Tools from multi-linear algebra can be used to develop simultaneous signal processing techniques across all the domains. In particular, we present tensor partial response signaling (TPRS) which allows the introduction of controlled interference within elements of a domain and also across domains. We develop the TPRS system using the tensor contracted convolution to generate a multi-domain signal with desired spectral and cross-spectral properties across domains. In addition, by studying the information theoretic properties of the multi-domain tensor channel, we present the trade-off between different domains that can be harnessed using this framework. Numerical examples for capacity and mean square error are presented to highlight the domain trade-off revealed by the tensor formulation. Furthermore, an application of the tensor framework to MIMO Generalized Frequency Division Multiplexing (GFDM) is also presented.

The Theory of Special Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Euler Equations ◽  
Lorentz Transformation ◽  
Electromagnetic Force ◽  
Momentum Tensor ◽  
Perfect Fluids ◽  
Dimensional Spacetime ◽  
Tensor Formulation ◽  
Basic Equations

This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, space and time are not separate entities. They are combined into a four-dimensional spacetime continuum, which is most clearly demonstrated in the formulation of the theory of special relativity due to Hermann Minkowski. The chapter then defines vectors and tensors with respect to the Lorentz transformation, leading to a tensor formulation of Maxwell's equations, of the electromagnetic force acting on charges and currents, and of the energy-momentum of the electromagnetic field and its conservation law. It also introduces the energy-momentum tensor of matter and discusses the basic equations of the hydrodynamics of perfect fluids (the Euler equations).

Tensor formulation of Hamilton’s equations

1988 ◽  
Vol 29 (9) ◽  
pp. 2001-2009 ◽  
Author(s):  
Paul H. Lim
Keyword(s):  
Tensor Formulation ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

scholarly journals Metric tensor formulation of strain in density-functional perturbation theory

2005 ◽  
Vol 71 (3) ◽  
Author(s):  
D. R. Hamann ◽  
Xifan Wu ◽  
Karin M. Rabe ◽  
David Vanderbilt
Keyword(s):  
Perturbation Theory ◽  
Density Functional ◽  
Metric Tensor ◽  
Density Functional Perturbation Theory ◽  
Tensor Formulation

scholarly journals Gravitational waves on Earth and their warming effects

2021 ◽  
Vol 13 (1) ◽  
pp. 43-54
Author(s):  
Horia DUMITRESCU ◽  
Vladimir CARDOS ◽  
Radu BOGATEANU
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Gravity Field ◽  
Space Time ◽  
Time Structure ◽  
Constant Light ◽  
Curved Space ◽  
Light Speed ◽  
Space Time Structure ◽  
Tensor Formulation

The gravity or reactive bundle energy is the outlet of the morphogenetic impact, known as “BIG BANG”, creating a bounded ordered/structured universe along with the solar system, including the EARTH-world with its human race. Post-impact, the huge kinetic energy is spread into stellar bodies associated with the light flux under strong mutual connections or gravitational bundle. Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures. Gravity according to the curved space-time theory is not seen as a gravitational force, but it manifests itself in the relativistic form of the space-time curvature needing the constancy of the light speed. But the constant light velocity makes the tidal wave/pulsating energy, a characteristic of solar energy, impossible. The Einstein’s field equation, expressed in terms of tensor formulation along with the constant light speed postulate, needs two special space-time tensors (curvature and torsion) in 4 dimensions, where for the simplicity the torsion/twist tensor is less well approximated (Bianchi identity) leading to a constant/frozen gravity (twist-free gravity).The non-zero torsion tensor plays a significant physical role in the planetary dynamics as a finest gear of a planet, where its spinning rotation is directly connected to the own work and space-time structure (or clock), controlled by light fluctuations (or tidal effect of gravity). The spin correction of Einstein’s gravitational field refers to the curvature-torsion effect coupled with fluctuating light speed. The mutual curvature-torsion bundle self-sustained by the quantum fluctuations of light speed engenders helical gravitational wave fields of a quantum nature where bodies orbit freely in the light speed field (cosmic wind). In contrast to the Einstein’s field equation describing a gravitational frozen field, a quantum tidal gravity model is proposed in the paper.

scholarly journals Unit vector template generator applied to a new control algorithm for an UPQC with instantaneous power tensor formulation, a simulation case study

2020 ◽  
Vol 10 (4) ◽  
pp. 3889
Author(s):  
Yeison Alberto Garcés Gómez ◽  
Nicolás Toro García ◽  
Fredy Edimer Hoyos
Keyword(s):  
Power Quality ◽  
Active Power Filter ◽  
Unit Vector ◽  
Active Power ◽  
Voltage Reference ◽  
Shunt Active Power Filter ◽  
Power Filter ◽  
Instantaneous Power ◽  
Tensor Formulation ◽  
Power Quality Conditioner

<span>In this paper we present a new algorithm to generate the reference signals to control the series and parallel power inverters in an unified power quality conditioner “UPQC” to enhance power quality. The algorithm is based in the instantaneous power tensor formulation which it is obtained by the dyadic product between the instantaneous vectors of voltage and current in n-phase systems. The perfect harmonic cancelation algorithm “PHC” to estimate the current reference in a shunt active power filter was modified to make it hardy to voltage sags through unit vector template generation “UVGT” while from the same algorithm it extracts the voltage reference for series active power filter. The model was validated by mean of simulations in Matlab-Simulink®.</span>

Solutions of Laplace's equation in an n-dimensional space of constant curvature

1939 ◽  
Vol 6 (1) ◽  
pp. 24-45 ◽  
Author(s):  
H. S. Ruse
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Christoffel Symbol ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Space Of Constant Curvature ◽  
Tensor Formulation ◽  
Classical Wave Equation ◽  
Image Position ◽  
Similar Solutions

This paper is a sequel to an earlier one containing a tensor formulation and generalisation of well-known solutions of Laplace's equation and of the classical wave-equation. The partial differential equation considered waswhere is the Christoffel symbol of the second kind, and the work was restricted to the case in which the associated line-elementwas that of an n-dimensional flat space. It is shown below that similar solutions exist for any n-dimensional space of constant positive or negative curvature K.

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