A passive scalar field convected by turbulence

Classical statistical mechanics is applied to the study of a passive scalar field convected by isotropic turbulence. A complete set of independent real parameters and dynamic equations are worked out to describe the dynamic state of the passive scalar field. The corresponding Liouville equation is solved by a perturbation method based upon a Langevin–Fokker–Planck model. The closure problem is treated by a variational approach reported in earlier papers. Two integral equations are obtained for two unknown functions: the scalar variance spectrum F(k) and the effective damping coefficient (k). The appearance of the energy spectrum of the velocity field in the two integral equations represents the coupling of the scalar field with the velocity field. As an application of the theory, the two integral equations are solved to derive the inertial-convective-range spectrum, obtaining F(k)=0.61 −1/3 k−5/3. Here is the dissipation rate of the scalar variance and is the dissipation rate of the energy of the velocity field. This theoretical value of the scalar Kolmogorov constant, 0.61, is in good agreement with experiments.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

The Relationship between Decision Trees and the Scale of Train Data Set

Decision Trees need train samples in the train data set to get classification rules. If the number of train data was too small, the important information might be missed and thus the model could not explain the classification rules of data. While it is not affirmative that large scale of train data set can get well model. This Paper analysis the relationship between decision trees and the train data scale. We use nine decision tree algorithms to experiment the accuracy, complexity and robustness of decision tree algorithms. Some results are demonstrated.

Basic equations for ferroelectrics

A set of new formula of energy functions for ferroelectrics was proposed, and then the new basic equations were derived in this paper. The finite element formulation based on the new basic equations was improved to avoid the equivalent nodal load produced by remnant polarization. With regard to the fundamentals of mathematics and physics, the new energy functions and basic equations are reasonable for the material element of ferroelectrics in finite element analysis.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Photoelectron angular distributions from above threshold ionization of hydrogen atoms in strong laser fields

We apply a scattering theory of nonperturbative quantum electrodynamics to study the photoelectron angular distributions (PADs) of a hydrogen atom irradiated by linearly polarized laser light. The calculated PADs show main lobes and jetlike structure. Previous experimental studies reveal that in a set of above-threshold-ionization peaks when the absorbed-photon number increases by one, the jet number also increases by one. Our study confirms this experimental observation. Our calculations further predict that in some cases three more jets may appear with just one-more-photon absorption. With consideration of laser-frequency change, one less jet may also appear with one-more-photon absorption. The jetlike structure of PADs is due to the maxima of generalized phased Bessel functions, not an indication of the quantum number of photoelectron angular momentum states.

Two-step digit-set-restricted modified signed-digit addition-subtraction algorithm and its optoelectronic implementation

A novel, to our knowledge, two-step digit-set-restricted modified signed-digit (MSD) addition-subtraction algorithm is proposed. With the introduction of the reference digits, the operand words are mapped into an intermediate carry word with all digits restricted to the set {(1) over bar, 0} and an intermediate sum word with all digits restricted to the set {0, 1}, which can be summed to form the final result without carry generation. The operation can be performed in parallel by use of binary logic. An optical system that utilizes an electron-trapping device is suggested for accomplishing the required binary logic operations. By programming of the illumination of data arrays, any complex logic operations of multiple variables can be realized without additional temporal latency of the intermediate results. This technique has a high space-bandwidth product and signal-to-noise ratio. The main structure can be stacked to construct a compact optoelectronic MSD adder-subtracter. (C) 1999 Optical Society of America.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Parallel optical negabinary signed-digit computing: algorithm and optical implementation

Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

One-step digit-set-restricted modified signed-digit adder using an incoherent correlator based on a shared content-addressable memory

An efficient one-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In this technique, carry propagation is avoided by introducing reference digits to restrict the intermediate carry and sum digits to {1,0} and {0,1}, respectively. The proposed technique requires significantly fewer minterms and simplifies system complexity compared to the reported one-step MSD addition techniques. An incoherent correlator based on an optoelectronic shared content-addressable memory processor is suggested to perform the addition operation. In this technique, only one set of minterms needs to be stored, independent of the operand length. (C) 2002 society or Photo-Optical Instrumentation Engineers.

Efficient two-step digit-set-restricted modified signed-digit algorithm based on optoelectronic shared content-addressable memory

A two-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In the proposed addition algorithm, carry propagation is avoided by using reference digits to restrict the intermediate MSD carry and sum digits into {(1) over bar ,0} and {0, 1}, respectively. The algorithm requires only 12 minterms to generate the final results, and no complementarity operations for nonzero outputs are involved, which simplifies the system complexity significantly. An optoelectronic shared content-addressable memory based on an incoherent correlator is used for experimental demonstration. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Efficient two-step digit-set-restricted modified signed-digit algorithm based on optoelectronic shared content-addressable memory

A two-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In the proposed addition algorithm, carry propagation is avoided by using reference digits to restrict the intermediate MSD carry and sum digits into {(1) over bar ,0} and {0, 1}, respectively. The algorithm requires only 12 minterms to generate the final results, and no complementarity operations for nonzero outputs are involved, which simplifies the system complexity significantly. An optoelectronic shared content-addressable memory based on an incoherent correlator is used for experimental demonstration. (c) 2005 Society of Photo-Optical Instrumentation Engineers.