Absence of Squirt Singularities for the Multi-Phase Muskat Problem

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.     

Contour Dynamics of Incompressible 3-D Fluids in a Porous Medium with Different Densities

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele–Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness when the smaller density is above (stable case) and in the unstable case we show ill-posedness.     

A New Maximum Principle for Impulsive First-Order Problems

We prove a new maximum principle for a boundaryvalue problem for first-order ordinary differentialequations with impulses at fixed moments.     

A Maximum Principle Applied to Quasi-Geostrophic Equations

We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of L^p-norms and asymptotic behavior of viscosity solution in the critical case. Our proofs are based on a maximum principle valid for more general flows.Partially supported by BFM2002-02269 grant.Partially supported by BFM2002-02042 grant.     

Improved Approach for the Maximum Entropy Deconvolution Problem

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.     

Existence of Weak Solutions for a Diffuse Interface Model for Viscous,Incompressible Fluids with General Densities

We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. In contrast to previous works, we study the general case that the fluids have different densities. This leads to an inhomogeneous Navier-Stokes system coupled to a Cahn-Hilliard system, where the density of the mixture depends on the concentration, the velocity field is no longer divergence free, and the pressure enters the equation for the chemical potential. We prove existence of weak solutions for the non-stationary system in two and three space dimensions.     

A Quantile General Index Derived from the Maximum Entropy Principle

We propose a linear separation method of multivariate quantitative data in such a way that the average of each variable in the positive group is larger than that of the negative group. Here, the coefficients of the separating hyperplane are restricted to be positive. Our method is derived from the maximum entropy principle. The composite score obtained as a result is called the quantile general index. The method is applied to the problem of determining the top 10 countries in the world based on the 17 scores of the Sustainable Development Goals (SDGs).     

A Frequency Localized Maximum Principle Applied to the 2D Quasi-Geostrophic Equation

In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces \mathringB^1-a_￥,q{\mathring{B}^{1-\alpha}_{\infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in \mathringB⁰_￥,q{\mathring{B}^{0}_{\infty,q}} for all 1 ≤ q < ∞. Here \mathringB^s_￥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of B^s_￥,q{B^{s}_{\infty,q}}.     

多组份流动质量分数保极值原理算法

对基于质量分数的Mie-Gruneisen状态方程多流体组份模型提出了新的数值方法.该模型保持混合流体的质量、动量、和能量守恒,保持各组份分质量守恒,在多流体组份界面处保持压力和速度一致.该模型是拟守恒型方程系统.对该模型系统的离散采用波传播算法.与直接对模型中所有守恒方程采用相同算法不同的是,在处理分介质质量守恒方程时,对波传播算法进行了修正,使之满足质量分数保极值原理.而不作修改的算法则不能保证质量分数在[0,1]范围.数值实验验证了该方法有效.     

Newtonian Dynamics from the Principle of Maximum Caliber

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle of maximum caliber (Jaynes, Phys Rev 106:620–630, 1957), when applied to the unknown trajectory followed by a particle, leads to Newton’s second law under two quite intuitive assumptions (both the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton’s equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others.     

Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM

We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation $−u''=f$ equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary lengths and polynomial degrees ($hp$-FEM). We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.     

Spatial Filtering of Signal Sources on the Basis of the Principle of Maximum Entropy in the Problem of Passive Direction Finding with Multibeam Antennas

Radiophysics and Quantum Electronics - We consider the methods of spatial filtering of input data used for passive monopulse direction finding. The algorithm of such filtering with employing the...     

On Polynomial Maximum Entropy Method for Classical Moment Problem

The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,$x$,$x^2$,···,$x^n$}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in [4]. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in [4] and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.     

The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations

The long time behavior of the solutions to the two dimensional dissipative quasi-geostrophic equations is studied. We obtain a new positivity lemma which improves a previous version of A. Cordoba and D. Cordoba [10] and [11]. As an application of the new positivity lemma, we obtain the new maximum principle, i.e. the decay of the solution in L^p for any p [2,+) when f is zero. As a second application of the new positivity lemma, for the sub-critical dissipative case with the existence of the global attractor for the solutions in the space H^s for any s>2(1–) is proved for the case when the time independent f is non-zero. Therefore, the global attractor is infinitely smooth if f is. This significantly improves the previous result of Berselli [2] which proves the existence of an attractor in some weak sense. For the case =1, the global attractor exists in H^s for any s0 and the estimate of the Hausdorff and fractal dimensions of the global attractor is also available.Acknowledgement The author thanks Prof. P. Constantin for encouragement and kind help for his research on the subject of 2D QG equations, Prof. J. Wu for useful conversation and Prof. A. Cordorba for providing preprints. This work was started while the author visited IPAM at UCLA with an IPAM fellowship. The hospitality and support of IPAM is gratefully acknowledged. This work is partially supported by the Oklahoma State University new faculty start-up fund and the Deans Incentive Grant.     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Air-Driven Segregation in Binary Granular Mixtures with Same Size but Different Densities

We investigate the segregation effect of binary granular mixtures with the same size but different densities under vibration at different air pressures. Our experiments show that the segregation state is seriously dependent on the air pressure and there is a new type of partially segregated state at high air pressure, which has the characteristic that the lighter grains tend to stay at the bottom and form a pure layer, while heavier grains and remained lighter ones tend to rise and to form a mixed layer on the top of the system. We redefine the order parameter to study the variation of the segregation effect with the air pressure and vibration parameter in detail. Finally, the mechanism of the air-driven segregation is illustrated by the faster acceleration due to the airflow through the granular bed for lighter particles.     

A Novel Method for the Assessment of Cortisol Hormone in Different Body Fluids Using A New Photo Probe Thiazole Derivative

A low cost and accurate method for the detection and analytical determination of the cortisol in pharmaceutical preparation, blood serum and urine was developed. The method was based upon the enhancement of fluorescence intensity of the band at 424 nm of the photo probe by different cortisol concentrations in acetonitrile at (pH 5.7, λ_ex?=?320 nm). The influence of the different parameters, e.g. pH, solvent, cortisol concentration and foreign ions concentrations that control the enhancement process of fluorescence intensity of the band of photo probe was critically investigated. The remarkable enhancement of the fluorescence intensity at 424 nm in acetonitrile by various concentrations of cortisol was successfully used as a photo- probe for the assessment of cortisol concentration. The calibration plot was achieved over the concentration range 8.0?×?10^?6–5.5?×?10^?9 mol L^?1 cortisol with a correlation coefficient of 0.998 and a detection limit of 4.7?×?10^?9 mol L^?1. The developed method is simple and proceeds without practical artifacts compared to the other determination methods.     

A Different Approach to the Multiplicity Problem in Hadron Collisions

The models frequently applied to estimate the target mass in high energy interactions are used in conjunction with the HEISENBERG formula to obtain a semi empirical formulation for multiplicity. It is seen that the experimental data obtained by us and other authors on multiplicity fit into that formulation when considering the initial colliding systems to be either π - p or π - π. Also the values of Cos θ (θ being the emission angle of the secondaries in lab system) averaged over all emitted particles estimated from the above formulation are in good agreement with our experimental data.     

基于最大隶属原则的核磁共振波谱模糊识别

介绍了基于最大隶属原则的核磁共振(NMR)波谱模糊识别原理与方法. 提出了关于核磁共振波谱模糊集合的概念,并给出了相应的隶属函数. 通过建立标准谱数据库和相应的模糊识别算法,实现了核磁共振波谱的快速自动定性分析. 对苯酚、邻苯二酚、间苯二酚及对苯二酚4种化合物及其11种混合物样品的¹H NMR谱进行了定性分析. 结果表明,在粗略找峰和隶属度阈值在0.45~0.85之间较大范围内取值的情况下,方法均给出了准确的识别结果.