scholarly journals Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Alessandro De Rosis ◽  
Kai H. Luo
Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.


Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 541 ◽  
Author(s):  
Venkata Kota ◽  
Narendra Chavda

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.


2018 ◽  
Vol 75 (10) ◽  
pp. 3521-3540 ◽  
Author(s):  
Etienne Dunn-Sigouin ◽  
Tiffany Shaw

Recent work has shown that extreme stratospheric wave-1 negative heat flux events couple with the troposphere via an anomalous wave-1 signal. Here, a dry dynamical core model is used to investigate the dynamical mechanisms underlying the events. Ensemble spectral nudging experiments are used to isolate the role of specific dynamical components: 1) the wave-1 precursor, 2) the stratospheric zonal-mean flow, and 3) the higher-order wavenumbers. The negative events are partially reproduced when nudging the wave-1 precursor and the zonal-mean flow whereas they are not reproduced when nudging either separately. Nudging the wave-1 precursor and the higher-order wavenumbers reproduces the events, including the evolution of the stratospheric zonal-mean flow. Mechanism denial experiments, whereby one component is fixed to the climatology and others are nudged to the event evolution, suggest higher-order wavenumbers play a role by modifying the zonal-mean flow and through stratospheric wave–wave interaction. Nudging all tropospheric wave precursors (wave-1 and higher-order wavenumbers) confirms they are the source of the stratospheric waves. Nudging all stratospheric waves reproduces the tropospheric wave-1 signal. Taken together, the experiments suggest the events are consistent with downward wave propagation from the stratosphere to the troposphere and highlight the key role of higher-order wavenumbers.


1983 ◽  
Vol 50 (3) ◽  
pp. 658-670 ◽  
Author(s):  
A. D. McClellan

The buccal mass of the gastropod Pleurobranchaea is used during a regurgitation response that consists of a writhing phase interrupted by brief periodic bouts of a vomiting phase (17, 20). During transitions from writhing to vomiting, specific changes occur in the motor pattern (19, 20). Evidence is presented suggesting that at least some of the initiation or "command" neurons for vomiting reside in the buccal ganglia. The present paper examines the role of two candidate vomiting-initiation cells, the ventral white cells (VWC) and midganglionic cells (MC), in the buccal ganglia of isolated nervous systems. Stimulation of single VWCs activates a vomiting motor pattern, consisting in part of alternating buccal root activity. Furthermore, the VWCs fire in high-frequency bursts during episodes (i.e., bouts) of this same vomiting pattern. Mutual reexcitation between the VWCs and motor pattern generator (MPG) appears to produce the accelerated buildup and maintenance of vomiting rhythms. Brief stimulation of single MCs "triggers" bouts of a vomiting motor pattern, but the membrane potential of this cell is only modulated during this same pattern, at least in the isolated nervous system. It is proposed that in intact animals the MCs are activated by sensory inputs and briefly excite the VWC-MPG network, thereby turning on the mutual reexcitatory mechanism mentioned above and switching the output pattern. A general implication for gastropod research is that higher order neurons that activate buccal root activity cannot automatically be given the function of "feeding command neuron," as some cells clearly control other responses, such as vomiting.


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