共查询到20条相似文献,搜索用时 15 毫秒
1.
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. 相似文献
2.
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. 相似文献
3.
We prove a new maximum principle for a boundaryvalue problem for first-order ordinary differentialequations with impulses at fixed moments. 相似文献
4.
5.
A Maximum Principle Applied to Quasi-Geostrophic Equations 总被引:16,自引:7,他引:9
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 Lp-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. 相似文献
6.
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. 相似文献
7.
Helmut Abels 《Communications in Mathematical Physics》2009,289(1):45-73
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. 相似文献
8.
Tomonari Sei 《Entropy (Basel, Switzerland)》2022,24(10)
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). 相似文献
9.
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
\mathringB1-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
\mathringBs¥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of Bs¥,q{B^{s}_{\infty,q}}. 相似文献
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11.
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. 相似文献
12.
Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM 下载免费PDF全文
Tomá &scaron Vejchodský & Pavel &Scaron olí n 《advances in applied mathematics and mechanics.》2009,1(2):201-214
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. 相似文献
13.
Morozov O. A. Fidelman V. R. Chumankin Yu. E. 《Radiophysics and Quantum Electronics》2019,62(2):133-141
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... 相似文献
14.
Jiu Ding Noah H. Rhee & Chenhua Zhang 《advances in applied mathematics and mechanics.》2016,8(1):117-127
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. 相似文献
15.
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 Lp 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 Hs 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 Hs 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. 相似文献
16.
Jan Korbel 《Entropy (Basel, Switzerland)》2021,23(1)
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. 相似文献
17.
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. 相似文献
18.
M. S. Attia E. El-Swafy A. O. Youssef H. A. Hefny M. H. Khalil 《Journal of fluorescence》2014,24(2):337-344
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, λex?=?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. 相似文献
19.
D. C. Ghosh A. Roychowdhury I. K. Daftari D. K. Bhattacharjee T. Roy 《Annalen der Physik》1978,490(1):15-18
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. 相似文献