Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

The diagnostics of density distribution for inhomogeneous dense DT plasmas using fast protons

The density distribution of inhomogeneous dense deuterium-tritium plasmas in laser fusion is revealed by the energy loss of fast protons going through the plasma. In our simulation of a plasma density diagnostics, the fast protons used for the diagnostics may be generated in the laser-plasma interaction. Dividing a two-dimensional area into grids and knowing the initial and final energies of the protons, we can obtain a large linear and ill-posed equation set. for the densities of all grids, which is solved with the Tikhonov regularization method. We find that the accuracy of the set plan with four proton sources is better than those of the set plans with less than four proton sources. Also we have done the density reconstruction especially. for four proton sources with and without assuming circularly symmetrical density distribution, and find that the accuracy is better for the reconstruction assuming circular symmetry. The error is about 9% when no noise is added to the final energy for the reconstruction of four proton sources assuming circular symmetry. The accuracies for different random noises to final proton energies with four proton sources are also calculated.

Tunable three-dimensional intensity distribution by a pure phase-shifting apodizer

The three-dimensional distribution of light intensity that is modulated by a pure phase-shifting apodizer is studied. Results show that the Strehl ratio can be altered by the proposed apodizer and by the waist width of incident Gaussian beams. By changing geometrical parameters of the proposed apodizer, we can increase the focal depth to several times that of the original system. The proposed apodizer can also be used to realize focal splitting and local minimum of intensity, which may be advantageous for constructing an optical trap. Furthermore, the local minimum of intensity number is tunable by changing the parameters of the apodizer. (c) 2005 Optical Society of America

Electroluminescence analysis and simulation of the effects of injection and temperature on carrier distribution in InGaN-based light-emitting diodes with color-coded quantum wells

This paper reports on an extensive analysis of the electroluminescence characteristics of InGaN-based LEDs with color-coded structure, i.e., with a triple quantum well structure in which each quantum well has a different indium content. The analysis is based on combined electroluminescence measurements and two-dimensional simulations, carried out at different current and temperature levels. Results indicate that (i) the efficiency of each of the quantum wells strongly depends on device operating conditions (current and temperature); (ii) at low current and temperature levels, only the quantum well closer to the p-side has a significant emission; (iii) emission from the other quantum wells is favored at high current levels. The role of carrier injection, hole mobility, carrier density and non-radiative recombination in determining the relative intensity of the quantum wells is discussed in the text. © 2013 The Japan Society of Applied Physics.

Theoretical analysis about the influence of channel layer thickness on the 2D electron gas and its distribution in InP-based high-electron-mobility transistors

The principle of high-electron-mobility transistor (HEMT) and the property of two-dimensional electron gas (2DEG) have been analyzed theoretically. The concentration and distribution of 2DEG in various channel layers are calculated by numerical method. Variation of 2DEG concentration in different subband of the quantum well is discussed in detail. Calculated results show that sheet electron concentration of 2DEG in the channel is affected slightly by the thickness of the channel. But the proportion of electrons inhabited in different subbands can be affected by the thickness of the channel. When the size of channel lies between 20-25 nm, the number of electrons occupying the second subband reaches the maximum. This result can be used in parameter design of materials and devices.

Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique

The mode characteristics of a three-dimensional (3D) microdisk with a vertical refractive index distribution of n(2)/3.4/n(2) are investigated by the S-matrix method and 3D finite-difference time-domain (FDTD) technique. For the microdisk with a thickness of 0.2 mu m. and a radius of 1 mu m, the mode wavelengths and quality factors for the HE7,1 mode obtained by 3D FDTD simulation and the S-matrix method are in good agreement as n(2) increases from 1.0 to 2.6. But the Q factor obtained by the 3D FDTD rapidly decreases from 1.12 X 10(4) to 379 as n2 increases from 2.65 to 2.8 owing to the vertical radiation losses, which cannot be predicted by the proposed S-matrix method. The comparisons also show that quality factors obtained from the analytical solution of two-dimensional microdisks under the effective index approximation are five to seven times smaller than those of the 3D FDTD as n(2) = 1 and R = 1 mu m. (c) 2006 Optical Society of America.

Influence of heated catalyzer on thermal distribution of substrate in HWCVD system

Based on Stefan-Boltzman and Lambert theorems, the radiation energy distribution on substrate (REDS) from catalyzer with parallel filament geometry has been simulated by variation of filament and system layout in hot-wire chemical vapor deposition. The REDS uniformity is sensitive to the distance between filament and substrate d(f-s) when d(f-s) less than or equal to 4 cm. As d(f-s) > 4 cm, the REDS uniformity is independent of d(f-s) and is mainly determined by filament number and filament separation. Two-dimensional calculation shows that the REDS uniformity is limited by temperature decay at filament edges. The simulation data are in good agreement with experiments. (C) 2003 Elsevier Science B.V. All rights reserved.

Temperature Distribution in Ridge Structure InGaN Laser Diodes and Its Influence on Device Characteristics

Time-dependent thermal simulation of ridge-geometry InGaN laser diodes is carried out with a two-dimensional model. A high temperature in the waveguide layer and a large temperature step between the regions under and outside the ridge are generated due to the poor thermal conductivity of the sapphire substrate and the large threshold current and voltage. The temperature step is thought to have a strong influence on the characteristics of the laser diodes. Time-resolved measurements of light-current curves,spectra, and the far-field pattern of the InGaN laser diodes under pulsed operation are performed. The results show that the thermal lensing effect improves the confinement of the higher order modes and leads to a lower threshold current and a higher slope efficiency of the device while the high temperature in the active layer results in a drastic decrease in the slope efficiency.

Influence of heated catalyzer on thermal distribution of substrate in HWCVD system

Based on Stefan-Boltzman and Lambert theorems, the radiation energy distribution on substrate (REDS) from catalyzer with parallel filament geometry has been simulated by variation of filament and system layout in hot-wire chemical vapor deposition. The REDS uniformity is sensitive to the distance between filament and substrate d(f-s) when d(f-s) less than or equal to 4 cm. As d(f-s) > 4 cm, the REDS uniformity is independent of d(f-s) and is mainly determined by filament number and filament separation. Two-dimensional calculation shows that the REDS uniformity is limited by temperature decay at filament edges. The simulation data are in good agreement with experiments. (C) 2003 Elsevier Science B.V. All rights reserved.

Numerical Study on the Distribution Characteristics of TP in Taihu Lake, China

A depth-averaged two-dimensional hydrodynamics model and a two-dimensional water quality model, bases on the alternating direction implicit (ADI) method, is developed to study the distribution characteristics of total phosphorus (TP) in Taihu Lake. Wind stress, the pollution source from the inflow rivers, releasing rate of TP from the bottom sediment and water diversion from Yangtze River are the effecting factors of TP distribution. By using the model proposed in this paper, the concentration field of the total phosphorus was simulated, which leads to the conclusion that the flow field has a great influence on the spatial and temporal distribution of TP in the Taihu Lake.

CFD-DEM simulation of three-dimensional aeolian sand movement

A three-dimensional CFD-DEM model is proposed to investigate the aeolian sand movement. The results show that the mean particle horizontal velocity can be expressed by a power function of heights. The probability distribution of the impact and lift-off velocities of particles can be described by a log-normal function, and that of the impact and lift-off angles can be expressed by an exponential function. The probability distribution of particle horizontal velocity at different heights can be described as a lognormal function, while the probability distribution of longitudinal and vertical velocity can be described as a normal function. The comparison with previous two-dimensional calculations shows that the variations of mean particle horizontal velocity along the heights in two-dimensional and three-dimensional models are similar. However, the mean particle density of the two-dimensional model is larger than that in reality, which will result in the overestimation of sand transportation rate in the two-dimensional calculation. The study also shows that the predicted probability distributions of particle velocities are in good agreement with the experimental results.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

Near-field distribution of optical transmission of periodic subwavelength holes in a metal film

Optical transmission of a two-dimensional array of subwavelength holes in a metal film has been numerically studied using a differential method. Transmission spectra have been calculated showing a significant increase of the transmission in certain spectral ranges corresponding to the excitation of the surface polariton Bloch waves on a metal surface with a periodic hole structure. Under the enhanced transmission conditions, the near-field distribution of the transmitted light reveals an intensity enhancement greater than 2 orders of magnitude in localized (similar to 40 nm) spots resulting from the interference of the surface polaritons Bragg scattered by the holes in an array.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.