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In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…
This work consists in the theorical development on the analysis of the Thermodynamic Laws and thermodynamic systems in relative motion, according to the laws of Classical Mechanics. The difference of this work for many of the literature is…
Trajectory planning in autonomous driving is highly dependent on predicting the emergent behavior of other road users. Learning-based methods are currently showing impressive results in simulation-based challenges, with transformer-based…
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are classified and a theorem on connection of them with point ones…
Some of the well-known experiments: the ''muon'' experiment, the Michelson-Morley type experiments, the Kennedy-Thorndike type experiments and the Ives-Stilwell type experiments are analyzed using the nonrelativistic theory, the ''apparent…
Integral transformations of the QCD invariant (running) coupling and of some related objects are discussed. Special attention is paid to the Fourier transformation, that is to transition from the space-time to the energy--momentum…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths…
In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines,…
With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found transformation of velocity from the laboratory system S to an accelerated, rotating frame of reference s. The physical sense of parameter entering into the LMN special…
Quantum mechanical systems with position dependent masses (PDM) admitting two parametric Lie symmetry groups are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a two parametric Lie group,…
Engines are systems and devices that convert one form of energy into another, typically into a more useful form that can perform work. In the classical setup, physical, chemical, and biological engines largely involve the conversion of heat…
A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate…
We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
This paper studies the tracking control problem for nonholonomic mobile robots based on second order dynamics, with application to consensus tracking and formation tracking. The greatest novelty in this paper is that the reference…
Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and realtime control strategy to dynamically correct the arbitrary type of errors in the system…
Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for…
The transition to a new low emission energy future results in a changing mix of generation and load types due to significant growth in renewable energy penetration and reduction in system inertia due to the exit of ageing fossil fuel power…
Particle-exchange machines utilize electronic transport to continuously transfer heat between fermionic reservoirs. Here, we couple a quantum mechanical resonator to a particle-exchange machine hosted in a quantum dot and let the system run…