Existence, uniqueness and travelling waves to model an invasive specie interaction with heterogeneous reaction and non-linear diffusion

<abstract><p>It is the objective to provide a mathematical treatment of a model to predict the behaviour of an invasive specie proliferating in a domain, but with a certain hostile zone. The behaviour of the invasive is modelled in the frame of a non-linear diffusion (of Porous Medium type) equation with non-Lipschitz and heterogeneous reaction. First of all, the paper examines the existence and uniqueness of solutions together with a comparison principle. Once the regularity principles are shown, the solutions are studied within the Travelling Waves (TW) domain together with stability analysis in the frame of the Geometric Perturbation Theory (GPT). As a remarkable finding, the obtained TW profile follows a potential law in the stable connection that converges to the stationary solution. Such potential law suggests that the pressure induced by the invasive over the hostile area increases over time. Nonetheless, the finite speed, induced by the non-linear diffusion, slows down a possible violent invasion.</p></abstract>

Effect of the finite speed of light in ionization of extended molecular systems

We study propagation effects due to the finite speed of light in ionization of extended molecular systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shrödinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the $$\hbox {H}_{2}^{+}$$ H 2 + molecular ion and the $$\hbox {Ne}_2$$ Ne 2 dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily accessible than the ground breaking synchrotron measurement by Grundmann et al. (Science 370:339, 2020).

Rhazes’ Contributions to Alchemy and Pharmacy

Context: Persia has been the cradle of science across human history. Many of today’s concepts in science, such as the finite speed of light and alcohol distillation, were first proposed by Persian scientists. Mohammad ibn Zakariya Razi (Rhazes) is undoubtedly one of the greatest Persian scientists over human history. Evidence Acquisition: In this paper, in addition to a brief review of the history of pharmacy and chemistry sciences in Persia, Rhazes’ valuable books in the fields of pharmacy and chemistry, along with a brief description of them, were introduced. Data were extracted from different historical and bibliography books and also the citation databases of PubMed, Scopus, and Google Scholar. Results: Rhazes’ books and treatises in the fields of pharmacy and chemistry have been classified into three categories: 1) the books and treatises containing some sections on pharmacy like Al-Hawi fi al-Tibb (Liber Continens) and Al-Mansouri fi al-Tibb, 2) those written merely on pharmacy, like Qarabadin (pharmacopeia), and 3) the books focusing on alchemy (kimia), like Sirr al-Asrar (Secret of secrets) and Al Asrar (Liber Secretorum). Three volumes of Al Hawi fi al-Tibb were applied as a reference in pharmacology in Western universities for many years. Sirr al-Asrar is his most important book on alchemy, describing raw materials used in alchemy, experimental apparatus necessary for alchemical investigations, and detailed procedures for the chemical manipulation of arsenic and sulfur. Conclusions: These valuable manuscripts demonstrate the ancient heritage of Persians and the great roles and contributions of Persian scientists in the history of science.

Effect of the finite speed of light in ionization of extended molecular systems

We study propagation effects due to the finite speed of light in ionization of extended molecular systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shrödinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the H + 2 molecular ion and the Ne 2 dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily affordable than the ground breaking synchrotron measurement by Grundmann et al [Science 370, 339 (2020)].

Radial component of vortex electric field force

he differential equations of motion of electrically charged bodies in an uneven vortex electric field at all possible range of velocities are obtained in the article. In the force interaction, in addition to the two components – the Coulomb and Lorentz forces – the third component of a hitherto unknown force is involved. This component turned out to play a crucial role in the dynamics of movement. The equations are written in the usual 3D Euclidean space and physical time.This takes into account the finite speed of electric field propagation and the law of electric charge conservation. On this basis, the trajectory of the electron in an uneven electric field generated by a positively charged spherical body is simulated. The equations of motion are written in vector and coordinate forms. A physical interpretation of the obtained mathematical results is given. Examples of simulations are given.

Optimization Modeling of Irreversible Carnot Engine from the Perspective of Combining Finite Speed and Finite Time Analysis

An irreversible Carnot cycle engine operating as a closed system is modeled using the Direct Method and the First Law of Thermodynamics for processes with Finite Speed. Several models considering the effect on the engine performance of external and internal irreversibilities expressed as a function of the piston speed are presented. External irreversibilities are due to heat transfer at temperature gradient between the cycle and heat reservoirs, while internal ones are represented by pressure losses due to the finite speed of the piston and friction. Moreover, a method for optimizing the temperature of the cycle fluid with respect to the temperature of source and sink and the piston speed is provided. The optimization results predict distinct maximums for the thermal efficiency and power output, as well as different behavior of the entropy generation per cycle and per time. The results obtained in this optimization, which is based on piston speed, and the Curzon–Ahlborn optimization, which is based on time duration, are compared and are found to differ significantly. Correction have been proposed in order to include internal irreversibility in the externally irreversible Carnot cycle from Curzon–Ahlborn optimization, which would be equivalent to a unification attempt of the two optimization analyses.

Gauge-Underdetermination and Shades of Locality in the Aharonov–Bohm Effect

I address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real (which I dub: ‘the potentials view’). I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into ‘gauge-underdetermination’: different gauge choices represent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature (or in classrooms), neither by proponents nor by opponents of the potentials view. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields (which I call the Wide Equivalence Class) is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory—an even narrower gauge equivalence relation—as the ontology of electrodynamics.

Effect of the Gravitational Aberration on the Earth Gravity Field

Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites.