scholarly journals Rigorous Asymptotic and Moment-Preserving Diffusion Approximations for Generalized Linear Boltzmann Transport in Arbitrary Dimension

2013 ◽  
Vol 42 (6-7) ◽  
pp. 237-297 ◽  
Author(s):  
Eugene d’Eon
Keyword(s):  
Arbitrary Dimension ◽  
Boltzmann Transport ◽  
Diffusion Approximations

scholarly journals Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type

2021 ◽  
Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial
Keyword(s):  
Projective Variety ◽  
Arbitrary Dimension ◽  
Smooth Projective Variety ◽  
The Other ◽  
Fano Variety ◽  
Fano Varieties ◽  
Intersection Product ◽  
Canonical Class ◽  
Main Input

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.

scholarly journals Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

2021 ◽  
Vol 58 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Jörn Sass ◽  
Dorothee Westphal ◽  
Ralf Wunderlich
Keyword(s):  
Stock Returns ◽  
Financial Market ◽  
Discrete Time ◽  
High Frequency ◽  
Utility Maximization ◽  
Limit Theorems ◽  
Approximate Solutions ◽  
Diffusion Approximations ◽  
Expert Opinions ◽  
Arrival Intensity

AbstractThis paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

scholarly journals Band degeneracy enhanced thermoelectric performance in layered oxyselenides by first-principles calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ning Wang ◽  
Menglu Li ◽  
Haiyan Xiao ◽  
Zhibin Gao ◽  
Zijiang Liu ◽  
...  
Keyword(s):  
Density Functional ◽  
Transport Theory ◽  
Relaxation Times ◽  
Wide Band ◽  
Type Systems ◽  
Model Systems ◽  
Boltzmann Transport ◽  
Seebeck Coefficients ◽  
Boltzmann Transport Theory ◽  
P Type

AbstractBand degeneracy is effective in optimizing the power factors of thermoelectric (TE) materials by enhancing the Seebeck coefficients. In this study, we demonstrate this effect in model systems of layered oxyselenide family by the density functional theory (DFT) combined with semi-classical Boltzmann transport theory. TE transport performance of layered LaCuOSe and BiCuOSe are fully compared. The results show that due to the larger electrical conductivities caused by longer electron relaxation times, the n-type systems show better TE performance than p-type systems for both LaCuOSe and BiCuOSe. Besides, the conduction band degeneracy of LaCuOSe leads to a larger Seebeck coefficient and a higher optimal carrier concentration than n-type BiCuOSe, and thus a higher power factor. The optimal figure of merit (ZT) value of 1.46 for n-type LaCuOSe is 22% larger than that of 1.2 for n-type BiCuOSe. This study highlights the potential of wide band gap material LaCuOSe for highly efficient TE applications, and demonstrates that inducing band degeneracy by cations substitution is an effective way to enhance the TE performance of layered oxyselenides.

scholarly journals Modelling with star-shaped distributions

2020 ◽  
Vol 8 (1) ◽  
pp. 45-69
Author(s):  
Eckhard Liebscher ◽  
Wolf-Dieter Richter
Keyword(s):  
Probabilistic Models ◽  
Arbitrary Dimension ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Range ◽  
Gaussian Density ◽  
Spherical Distributions ◽  
Data Points ◽  
Non Gaussian ◽  
General Method

AbstractWe prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

scholarly journals Universal mobility characteristics of graphene originating from charge scattering by ionised impurities

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jonathan H. Gosling ◽  
Oleg Makarovsky ◽  
Feiran Wang ◽  
Nathan D. Cottam ◽  
Mark T. Greenaway ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Carrier Density ◽  
Carrier Mobility ◽  
Carrier Transport ◽  
Analytical Models ◽  
Pristine Graphene ◽  
High Electron ◽  
Boltzmann Transport ◽  
Transport Parameters ◽  
Wide Range

AbstractPristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and provides a way to predict a priori all key transport parameters of graphene devices. Our results open a route for controlling the transport properties of graphene by doping and for engineering the properties of 2D materials and heterostructures.

scholarly journals Electron liquid state in the symmetric Anderson lattice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor N. Karnaukhov
Keyword(s):  
Low Temperatures ◽  
Arbitrary Dimension ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Anomalous Behavior ◽  
Effective Field ◽  
Kondo Lattice ◽  
Field Approach ◽  
Cubic Lattices ◽  
Half Filling

AbstractUsing mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $$\mathbf{k} $$ k and $$\mathbf{k} +\overrightarrow{\pi }$$ k + π → , the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

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