Modeling AlGaN p-i-n photodiodes

Ternary AlGaN alloys with a band gap of 3.4 to 6.2 eV are very promising for photodetectors in the UV wavelength range. Using the COMSOL MULTIPHYSICS software based on AlGaN, a p-i-n photodiode model was developed, including its I–V characteristic, spectral sensitivity of the received radiation, absorption coefficient as a function of the aluminum fraction and the depletion layer thickness. To calculate the process of interaction of a semiconductor with EM radiation, we used a model based on the use of an element of the transition matrix through the carrier lifetime during spontaneous recombination. In this case, the peak sensitivity of the photodiode is from 0.08 to 0.18 A/W at wavelengths of 0.2–0.33 µm. This is in line with experimental results taken from the relevant literature.

GENERATION OF WIND-SERIES USING CUMULATIVE PROBABILITY WIND TRANSITION MATRIX-A FIRST ORDER MARKOV PROCESS

One appl ica tion ofihe cuuiulative probability wind tra ns ition matrix is 10 determine the variousprnhal"lk ....i n,1....-ries th ai mi1;\'hl occur. during the period fur which offs hore oilspil1 risk is 10 be analysed. Du ring th is;Inalpli ~ ""'t" haw to gene la te different probable "';110.1 conditions at d iff erent Instances oftime. OnC" ur lhe method s tosiumlutcthe nl lhlu m wind behaviourt hrough lime. is 10 U ~ h istorical wi nd da ta presented in the fon n of wi nd Ira n...ilion lItutrix. Th is pa per h it;hli.::hts th r- 1llC'l h(Klulog)' and use ofthe cumulat ive probability v.i nd transition matrix. in~t'lh"ral ill~ 1111' ,Iifferl:'nl proba ble wind-series.

A weighted graph zeta function involved in the Szegedy walk

We define a new weighted zeta function for a finite graph and obtain its determinant expression. This result gives the characteristic polynomial of the transition matrix of the Szegedy walk on a graph.

Island for gravitationally prepared state and pseudo entanglement wedge

We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra-ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

Method of lines for solving linear equations of mathematical physics with the third and first types boundary conditions

The use of the method of lines in solving multidimensional problems of mathematical physics makes it possible to eliminate the discrepancies caused by the use of the sweep method in certain coordinates. As a result, the solution of the Poisson equation, for example, is obtained without using the relaxation method. In the article, the problem on the eigenvalues and vectors of the transition matrix is solved for boundary conditions of the third and first types, used to solve a one-dimensional equation of parabolic type by the method of lines. Due to the features of boundary conditions of the third type for determining the eigenvalues, a mixed method was proposed based on the Vieta theorem and the representation of the characteristic equation in trigonometric form typical for the method of lines. To solve the eigenvector problem, a simple sweep method was used with the algebraic compliments to the transition matrix. Discontinuous solutions of a one-dimensional parabolic equation were presented for various values of complex 1 -αl; the method for solving the characteristic equation was selected based on these values. The calculation results are in good agreement with the analytical solution.

Effects of Different Mutation Rates and Randomness on the Distribution of Linkage Disequilibrium

Background Mutation has recently received much attention on its role in the evolution and genetics of complex trait. The linkage disequilibrium (LD) distribution can be affected by mutation as reported recently, in which the same mutation rates were adopted in the transition matrix. However, effects of different types, rates and randomness of mutation on LD distribution remain unexplored. Results Here, we considered in the transition matrix mutations at each locus to be of different types and rates (i.e. nucleotide transition or transversion treated differently), to examine how the LD distribution between two genetic loci was affected. After examining consecutively factors such as effective population size, recombination and selection, different mutation types and rates could further change the dynamics of LD distribution. However, at the current scale of mutation rate (weak at 10−9-10−8), mutation seemed to play only a minor role, compared to recombination and selection. A simple model further showed that mutation randomness increased the ruggedness of LD curves, which fluctuated around the steady state. Conclusions Taken together, different mutation rates and randomness could further disturb the dynamics of LD distribution. Our findings can help better understand the role of mutation in molecular evolution and complex trait genetics.

The Predictive Power of Transition Matrices

When working with Markov chains, especially if they are of order greater than one, it is often necessary to evaluate the respective contribution of each lag of the variable under study on the present. This is particularly true when using the Mixture Transition Distribution model to approximate the true fully parameterized Markov chain. Even if it is possible to evaluate each transition matrix using a standard association measure, these measures do not allow taking into account all the available information. Therefore, in this paper, we introduce a new class of so-called "predictive power" measures for transition matrices. These measures address the shortcomings of traditional association measures, so as to allow better estimation of high-order models.

The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media

Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.