scholarly journals The MGT-Fourier model in the supercritical case

2021 ◽  
Vol 301 ◽  
pp. 543-567
Author(s):  
Monica Conti ◽  
Lorenzo Liverani ◽  
Vittorino Pata
Keyword(s):  
Supercritical Case ◽  
Fourier Model

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

scholarly journals ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 549-575 ◽  
Author(s):  
J. COLLIANDER ◽  
S. IBRAHIM ◽  
M. MAJDOUB ◽  
N. MASMOUDI
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Supercritical Case ◽  
Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

scholarly journals Skeletons of Near-Critical Bienaymé-Galton-Watson Branching Processes

2015 ◽  
Vol 47 (2) ◽  
pp. 530-544
Author(s):  
Serik Sagitov ◽  
Maria Conceição Serra
Keyword(s):  
Critical Case ◽  
Branching Processes ◽  
Threshold Value ◽  
High Threshold ◽  
Birth Process ◽  
Birth And Death Processes ◽  
Supercritical Case ◽  
Natural Choice ◽  
Future Reproduction ◽  
Asymptotic Representations

Skeletons of branching processes are defined as trees of lineages characterized by an appropriate signature of future reproduction success. In the supercritical case a natural choice is to look for the lineages that survive forever (O'Connell (1993)). In the critical case it was suggested that the particles with the total number of descendants exceeding a certain threshold could be distinguished (see Sagitov (1997)). These two definitions lead to asymptotic representations of the skeletons as either pure birth process (in the slightly supercritical case) or critical birth-death processes (in the critical case conditioned on the total number of particles exceeding a high threshold value). The limit skeletons reveal typical survival scenarios for the underlying branching processes. In this paper we consider near-critical Bienaymé-Galton-Watson processes and define their skeletons using marking of particles. If marking is rare, such skeletons are approximated by birth and death processes, which can be subcritical, critical, or supercritical. We obtain the limit skeleton for a sequential mutation model (Sagitov and Serra (2009)) and compute the density distribution function for the time to escape from extinction.

Branching processes with varying and random geometric offspring distributions

1975 ◽  
Vol 12 (01) ◽  
pp. 135-141 ◽  
Author(s):  
Niels Keiding ◽  
John E. Nielsen
Keyword(s):  
Asymptotic Behavior ◽  
Generating Functions ◽  
Conditional Expectation ◽  
Elementary Proof ◽  
Branching Processes ◽  
Random Environments ◽  
Subcritical Case ◽  
Supercritical Case ◽  
Extinction Probabilities ◽  
Varying Environments

The class of fractional linear generating functions is used to illustrate various aspects of the theory of branching processes in varying and random environments. In particular, it is shown that Church's theorem on convergence of the varying environments process admits of an elementary proof in this particular case. For random environments, examples are given on the asymptotic behavior of extinction probabilities in the supercritical case and conditional expectation given non-extinction in the subcritical case.

Tension and Stress Calculations in a 3-D Fourier Model of Gall Bladder Geometry Obtained from MR Images

2004 ◽  
Vol 32 (5) ◽  
pp. 744-755 ◽  
Author(s):  
D. Liao ◽  
B. U. Duch ◽  
H. Stødkilde-Jørgensen ◽  
Y. J. Zeng ◽  
H. Gregersen ◽  
...  
Keyword(s):  
Gall Bladder ◽  
Mr Images ◽  
Fourier Model

scholarly journals Reduced-Order Modeling of Stratospheric Winds and Its Application in High-Altitude Balloon Trajectory Simulations

2017 ◽  
Vol 56 (6) ◽  
pp. 1753-1766 ◽  
Author(s):  
Sai Sudha Ramesh ◽  
Kian Meng Lim ◽  
Heow Pueh Lee ◽  
Boo Cheong Khoo
Keyword(s):  
High Altitude ◽  
Weather Conditions ◽  
Temporal Variations ◽  
Weather Data ◽  
Compact Representation ◽  
Station Keeping ◽  
Quasi Biennial Oscillation ◽  
Wind Profiles ◽  
Fourier Model ◽  
Trajectory Simulations

AbstractThe knowledge of weather conditions at the stratosphere is important for the planning and execution of high-altitude balloon flights, which require an accurate modeling of weather data over a period of time. Various methods based on statistical analysis, artificial neural networks, and cluster analysis have been employed to model the temporal variation of weather parameters. In the present study, a proper orthogonal decomposition (POD) method has been used to study the spatial as well as temporal variations of wind data in Singapore. The use of POD facilitates a compact representation of the weather dataset and aids in faster computation of wind profiles for use in balloon trajectory simulation. Further, the results reveal the existence of the quasi-biennial oscillation phenomenon, which is characteristic of equatorial easterly–westerly winds. This phenomenon enables the development of a Fourier prediction model, which can be used in real-time balloon trajectory simulations. The Fourier model is observed to be sensitive to wind velocity fluctuations, especially in the vicinity of alternating wind directions. However, it provides a reasonable projection of balloon trajectory, which can be used in preliminary planning and testing of high-altitude flights. Thus, a prior knowledge of wind profiles based on POD or a Fourier model aids in balloon station keeping. A simple case of altitude-controlled balloon flight is presented, and the results highlight the advantages of the present method in balloon station keeping.

Convergence of general branching processes and functionals thereof

1974 ◽  
Vol 11 (03) ◽  
pp. 471-478 ◽  
Author(s):  
Peter Jagers
Keyword(s):  
Wide Class ◽  
Random Function ◽  
Branching Processes ◽  
Supercritical Case ◽  
Age Dependent ◽  
Dependent Property ◽  
Number Of Individuals

With each individual in a branching population associate a random function of the age. Count the population by the values of these functions. Different choices yield different processes. In the supercritical case a unified treatment of the asymptotics is possible for a wide class, including for example the number of individuals having some random age dependent property or integrals of branching processes. As an application, the demographic concept of average age at childbearing is given a rigorous interpretation.

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