Scaling dependence on time and distance in nonlinear fractional diffusion equations and possible applications to the water transport in soils

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different physical systems like: amorphous semicondutors, polymers, composite heterogeneous films and porous media. They have also been used to calculate the heat load intensity change in blast furnace walls, to solve problems of control theory \ and dynamic problems of linear and nonlinear hereditary mechanics of solids. In this work, we investigate the scaling properties related to the nonlinear fractional diffusion equations and indicate the possibilities to the applications of these equations to simulate the water transport in unsaturated soils. Usually, the water transport in soils with anomalous diffusion, the dependence of concentration on time and distance may be expressed in term of a single variable given by $\lambda _{q}=x/t^{q}.$ In particular, for $q=1/2$ the systems obey Fick's law and Richards' equation for water transport. We show that a generalization of Richards' equation via fractional approach can incorporate the above property.Comment: 9 page

Cutting plane methods for general integer programming

Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method. In this method, linear constraints are added to the associated linear programming (LP) problem until an integer optimal solution is found. These constraints cut off part of the LP solution space but do not eliminate any feasible integer solution. In this report algorithms for solving IP due to Gomory and to Dantzig are presented. Two other cutting plane approaches and two extensions to Gomory's algorithm are also discussed. Although these methods are mathematically elegant they are known to have slow convergence and an explosive storage requirement. As a result cutting planes are generally not computationally successful

Warehouse commodity classification from fundamental principles. Part I: Commodity & burning rates

An experimental study was conducted to investigate the burning behavior of an individual Group A plastic commodity over time. The objective of the study was to evaluate the use of a nondimensional parameter to describe the time-varying burning rate of a fuel in complex geometries. The nondimensional approach chosen to characterize burning behavior over time involved comparison of chemical energy released during the combustion process with the energy required to vaporize the fuel, measured by a B-number. The mixed nature of the commodity and its package, involving polystyrene and corrugated cardboard, produced three distinct stages of combustion that were qualitatively repeatable. The results of four tests provided flame heights, mass-loss rates and heat fluxes that were used to develop a phenomenological description of the burning behavior of a plastic commodity. Three distinct stages of combustion were identified. Time-dependent and time-averaged B-numbers were evaluated from mass-loss rate data using assumptions including a correlation for turbulent convective heat transfer. The resultant modified B-numbers extracted from test data incorporated the burning behavior of constituent materials, and a variation in behavior was observed as materials participating in the combustion process varied. Variations between the four tests make quantitative values for each stage of burning useful only for comparison, as errors were high. Methods to extract the B-number with a higher degree of accuracy and future use of the results to improve commodity classification for better assessment of fire danger are discussed. © 2011 Elsevier Ltd. All rights reserved

Dynamic Structure Function in 3he-4he Mixtures

Relevant features of the dynamic structure function $S(q,\omega)$ in $^3$He-$^4$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to $S(q,\omega)$, coming from $^3$He and $^4$He elementary excitations, as well as to explore the role of the cross term $S^{(3,4)}(q,\omega)$. Both the low-$q$ (phonon-roton $^4$He excitations and 1p-1h $^3$He excitations) and high-$q$ (deep inelastic scattering) ranges are discussed.Comment: 29 pages, Plain TeX, 11 figures available by request from [email protected]

Integro-differential diffusion equation for continuous time random walk

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution.Comment: 12 page

Surfactant adsorption density calculation from Fourier transform infrared external reflection spectroscopy (FTIR/ERS)

Journal ArticleAn equation to calculate surfactant adsorption density from Fourier transform infrared external reflection spectra was established. The derivation and limitation of this equation are discussed in detail. The validation of the FTIR/ERS adsorption density equation was experimentally verified from the analysis of Langmuir-Blodgett films of stearic acid with and without calcium ions in the subphase at the air-water interface and at fluorite surface. In this way the properties of Langmuir- Blodgett films at the air-water interface are further characterized using FTIR/ERS

State estimation from pair of conjugate qudits

We show that, for $N$ parallel input states, an anti-linear map with respect to a specific basis is essentially a classical operator. We also consider the information contained in phase-conjugate pairs $|\phi > |\phi^*>$, and prove that there is more information about a quantum state encoded in phase-conjugate pairs than in parallel pairs.Comment: 4 pages, 1 tabl

Broad class of nonlinear Langevin equations with drift and diffusion cofficients separable in time and space: Generalized n-moment, ergodicity, Einstein relation and fluctuations of the system

A wide class of nonlinear Langevin equations with drift and diffusion coefficients separable in time and space driven by the Gaussian white noise is analyzed in terms of a generalized n-moment. We show the system may present ergodic property, a key property in statistical mechanics, for space-time-dependent drift and diffusion coefficients. A generalized Einstein relation is also obtained. Besides, we show that the first two generalized moments and variance are useful to describe the drift and fluctuations of the system.Comment: 22 pages, 4 figure

Numerical simulation of flow surrounding a thermoacoustic stack:single-stack against double-stack plate domain

Over the last few decades, numerical simulation has fast become an effective research tool in analyzing internal and external fluid flow. Much of the unknowns associated with microscopic bounded and unbounded fluid behavior generally not obtainable via experimental approach can now be explained in details with computational fluid dynamics modeling. This has much assist designers and engineers in developing better engineering designs. However, the choice of the computational domain selected plays an important role in exhibiting the correct flow patterns associated with changes in certain parameters. This research looked at the outcomes when two computational domains were chosen to represent a system of parallel stack plates in a thermoacoustic resonator. Since the stack region is considered the “heart” of the system, accurate modeling is crucial in understanding the complex thermoacoustic solid-fluid interactions that occur. Results showed that although the general flow pattern and trends have been produced with the single and double plate stack system, details of a neighboring solid wall do affect the developments of vortices in the stack region. The symmetric assumption in the computational domain may result in the absence of details that could generate an incomplete explanation of the patterns observed such as shown in this study. This is significant in understanding the solid-fluid interactions that is thermoacoustic phenomena