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An Unexpected Renaissance Age
Published in Alessio Plebe, Pietro Perconti, The Future of the Artificial Mind, 2021
Alessio Plebe, Pietro Perconti
On a side very different from mathematical topology, there are intriguing attempts at explaining DL by drawing an analogy with theoretical physics. There is a technique, known as renormalization group, which has played a fundamental role in contemporary theoretical physics, overcoming the problem of series summing up to infinite probability in fundamental equations, like Dirac’s quantum electrodynamics (Stueckelberg and Petermann, 1953). The renormalization group allows one to relate changes of a physical system that appear at different scales, yet exhibit scale invariance properties. By applying renormalization group it was possible to resolve the critical divergence towards infinity of the series in the Dirac equation. The renormalization group is also the best tool for the analysis of critical phenomena, phase transitions at the boundaries between the ordinary discontinuous behavior between phases, and the continuum of phases observed at temperatures above a certain threshold. Physical systems approaching the critical point have a remarkable invariance in scale of some of their parameters, making the renormalization group very effective in connecting phenomena which occur at quite different length scales (Wilson and Kogut, 1974). What does the renormalization group have to do with artificial neural networks?
Three Dimensional Modelling of Seismicity In Deep Level Mines
Published in Hans-Peter Rossmanith, Mechanics of Jointed and Faulted Rock, 2018
For mine design purposes it is very desirable to represent stress transfer and seismic recurrence effects as a definite mechanistic (though not necessarily deterministic) process which can be analysed numerically in routine mine design studies. One of the major challenges in reaching this goal is the ability to model large scale damage, recognizing that fracturing occurs on a multiplicity of length scales. The essence of the problem, therefore, is not merely to implement efficient numerical solution procedures for large systems of equations but, in addition, to be able to represent the self-organizing fracture coalescence processes on many scales. A number of attempts to address these goals have been made using renormalization solution concepts (Madden 1983, Allegre et. al. 1995, Main 1995) based on concepts of critical phenomena in physics (Wilson 1979). This paper presents some initial steps towards the formulation of a general solution scheme which incorporates time dependent stress relaxation effects in a three dimensional model and which also allows hierarchical failure processes to be modelled by approximating the inelastic strain in a given region as a special set of appropriately aligned crack elements. Failure is represented by means of discontinuity elements at multiple hierarchical levels, enabling fracture coalescence and clustering to be manifested at all scales. The formulation of the time dependent stress relaxation model is first discussed, followed by a suggested scheme for the allocation of the equivalent crack elements.
Influence of Carrier Localization on Efficiency Droop and Stimulated Emission in AlGaN Quantum Wells
Published in Zhe Chuan Feng, Handbook of Solid-State Lighting and LEDs, 2017
A valuable insight into the influence of carrier localization on PL efficiency can be obtained by PL spectroscopy at low temperatures. It is demonstrated that the excitation power density dependence of the PL band peak position has a nonmonotonous shape, as illustrated in Figure 11.19 [103]. The peak redshifts at low excitations reaches the minimum and starts blueshifting afterward. The origin of the redshift with increasing carrier density can be caused by two processes: the bandgap renormalization and the carrier redistribution within localized states. The bandgap renormalization due to many-body interaction can be excluded, since the effect is strongly reduced by carrier localization [104,105], which is important in AlGaN at low temperatures and excitations. Moreover, according to the experimental conditions, the redshift starts already at quite low carrier density of ~1017 cm−3, that is, is well below the density sufficient for significant bandgap renormalization. Consequently, the carrier redistribution within localized states is a more probable origin of the band redshift than the bandgap renormalization.
Impact of Electron-Phonon Interaction on Thermal Transport: A Review
Published in Nanoscale and Microscale Thermophysical Engineering, 2021
Yujie Quan, Shengying Yue, Bolin Liao
It was not until the development of accurate first-principles calculations for phonon-phonon [33, 34] and electron-phonon interactions [35] that the effect of EPI on phonon transport can be thoroughly evaluated in an extended range of materials, demonstrating that the thermal conductivity in solids can be strongly modified by the scattering of phonons by a high concentration of electrons [23], as well as the change of the phonon frequencies (“renormalization”) due to EPI. The influence of EPI on phonon transport has been studied in several heavily doped materials through investigations of the dependence of their lattice thermal conductivity on carrier concentration. Furthermore, recent studies on the thermal conductivity of metals have shown that in certain transition metals, the lattice thermal conductivity is non-negligible compared with the electronic thermal conductivity [36]. In these metals, EPI plays an important role in determining phonon scattering rates and thus can impact the overall thermal transport.
AlB2 and MgB2: a comparative study of their electronic, phonon and superconductivity properties via first principles
Published in Philosophical Magazine, 2020
Cai Cheng, Man-Yi Duan, Zhao Wang, Xiao-Lin Zhou
The phonon anomaly of the AlB2-type structure is also called Kohn anomaly, and the Tc can be estimated by Kohn anomaly for AlB2-type structure [17]. Doing of 25% of Al into MgB2 will result in phonon and electron–phonon renormalization with the strongest phonon frequency renormalization [18,19]. The influence of Al and C doping on the electronic structure and phonon renormalization in MgB2 [20] indicates that the transition temperature of MgB2 decreases by partial substitution of Mg for Al. Moreover, the superconductivity is totally suppressed by Al content of 10% [21]. In addition, three-gap superconductivity in monolayer MgB2 has been observed by solving the anisotropic Eiliashberg equations, and it is very robust with the temperature, even at the critical temperature of 20 K [22]. And AlB2 and MgB2 are also excellent thermoelectricity [23,24].
Thermodynamics of quantum lattice system with local multi-well potentials: dipole ordering and strain effects in modified Blume–Emery–Griffiths model
Published in Phase Transitions, 2019
Taking this effect into account in the framework of the lattice version of the BEG model, one should consider deformation of the crystal lattice (caused by an external factor) as an immediate reason of variation of local potentials (and, thus, the energy gap ). In this connection the initial Hamiltonian (1) should be supplemented by a respective termtaking into account the renormalization of the energy gap due to deformation(here is a relative change of the volume) as well as the energy of an elastic deformation ( is the volume elastic constant, v is the volume related to the one formula unit, N is the number of structure elements described by the locally anharmonic potentials), while D is the constant of an electron-deformational interaction.