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A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
It can be agreed that the linear superposition and energy conservation are two independent physics laws in general. The former allows the energy to be re-distributed over space and the latter restricts the energy in the total amount.…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the…
From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain, and fractional order…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
The superposition law (SL) sums the components of electromagnetic (EM) waves at each spatial point when these waves meet in space. In contrast, the energy conservation law requires energy to be summed in the quadratic form of the EM fields.…
Of particular interest for radio and hard X-ray diagnostics of accelerated electrons during solar flares is the understanding of the basic non-linear mechanisms regulating the relaxation of electron beams propagating in turbulent plasmas.…
The article presents four identities containing the spatio-temporal differential operator also known as four-divergence. These equations are used to prove the invariance of wave equation under orthogonal paravector transformations.…
Three thought experiments demonstrate that under certain circumstances electromagnetic fields have to be attenuated or amplified multiplicatively in order not to violate the conservation of energy. Modulation of radiation by means other…
In the context of the so called ``membrane paradigm'' of black holes/branes, it has been known for sometime that the dynamics of small fluctuations on the stretched horizon can be viewed as corresponding to diffusion of a conserved charge…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
We study the isentropic compressible Euler equations in multi-dimensions with stochastic perturbation of transport type. On the one hand, this is motivated by the physical modelling in turbulence theory. On the other hand, it has been shown…
Mathematical modeling of bodily tides can be carried out in various ways. Most straightforward is the method of complex amplitudes, which is often used in the planetary science. Another method, employed both in planetary science and…
The idea of using metaplastic synapses to incorporate the separate storage of long- and short-term memories via an array of hidden states was put forward in the cascade model of Fusi et al. In this paper, we devise and investigate two…
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time- convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in…
We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time…