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Register a new userEmpirical relationship as a stepping-stone to theory
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Added by
Marjan Ribari\\v{c} Prof.
Publication date
2021
fields
Physics
and research's language is
English
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We consider parsimonious construction of empirical equations, to promote interest in them as a stepping-stone model to the physical law. To this end, we provide a variety of historical examples and simulate a parsimonious empirical calculation of Planck law, and of van der Waals equation. Thereby we provide a) Empirical forms of Planck law, and b) Collation of verified symmetries and catastrophes-like properties of empirical P-T surface of real gases. An empirical equation of state for a real gas should take account of these properties.
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As 5th Generation research reaches the twilight, the research community must go beyond 5G and look towards the 2030 connectivity landscape, namely 6G. In this context, this work takes a step towards the 6G vision by proposing a next generation communication platform, which aims to extend the rigid coverage area of fixed deployment networks by considering virtual mobile small cells (MSC) that are created on demand. Relying on emerging computing paradigms such as NFV (Network Function Virtualization) and SDN (Software Defined Networking), these cells can harness radio and networking capability locally reducing protocol signaling latency and overhead. These MSCs constitute an intelligent pool of networking resources that can collaborate to form a wireless network of MSCs providing a communication platform for localized, ubiquitous and reliable connectivity. The technology enablers for implementing the MSC concept are also addressed in terms of virtualization, lightweight wireless security, and energy efficient RF. The benefits of the MSC architecture towards reliable and efficient cell offloading are demonstrated as a use-case.
Researchers have found that the metabolisms of organisms appear to scale proportionally to a 3/4 power of their mass. Mathematics in this article suggests that the capacity of an isotropically radiating energy supply scales up by a 4/3 power as its size (and therefore the degrees of freedom of its circulatory system) increases. Accordingly, cellular metabolism scales inversely by a 3/4 power, likely to prevent the 4/3 scaling up of the energy supply overheating the cell. The same 4/3 power scaling may explain cosmological dark energy.
Consider a one-dimensional stepping stone model with colonies of size $M$ and per-generation migration probability $ u$, or a voter model on $mathbb{Z}$ in which interactions occur over a distance of order $K$. Sample one individual at the origin and one at $L$. We show that if $M u/L$ and $L/K^2$ converge to positive finite limits, then the genealogy of the sample converges to a pair of Brownian motions that coalesce after the local time of their difference exceeds an independent exponentially distributed random variable. The computation of the distribution of the coalescence time leads to a one-dimensional parabolic differential equation with an interesting boundary condition at 0.
We present a microwave spectral taxonomy study of several hydrocarbon/CS$_2$ discharge mixtures in which more than 60 distinct chemical species, their more abundant isotopic species, and/or their vibrationally excited states were detected using chirped-pulse and cavity Fourier-transform microwave spectroscopies. Taken together, in excess of 85 unique variants were detected, including several new isotopic species and more than 25 new vibrationally excited states of C$_2$S, C$_3$S, and C$_4$S, which have been assigned on the basis of published vibration-rotation interaction constants for C$_3$S, or newly calculated ones for C$_2$S and C$_4$S. On the basis of these precise, low-frequency measurements, several vibrationally exited states of C$_2$S and C$_3$S were subsequently identified in archival millimeter-wave data in the 253--280 GHz frequency range, ultimately providing highly accurate catalogs for astronomical searches. As part of this work, formation pathways of the two smaller carbon-sulfur chains were investigated using $^{13}$C isotopic spectroscopy, as was their vibrational excitation. The present study illustrates the utility of microwave spectral taxonomy as a tool for complex mixture analysis, and as a powerful and convenient `stepping stone to higher frequency measurements in the millimeter and submillimeter bands.
Applying the resolution-scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Ito process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker-Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrodinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we identify a generalization to time dependent problems in any number of dimensions. The Ito process is then driven by a function which is identified as establishing the link between non-differentiable dynamics and standard quantum mechanics. This is the basis for the scale relativistic interpretation of standard quantum mechanics and, in the case of applications to chaotic systems, it leads us to identify quantum-like states as characterizing the entire system rather than the motion of its individual constituents.
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