Solutions of the telegrapher's equation in the presence of traps

Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

Boundary between Soil and Saprolite in Alisols in the South of Brazil

Despite numerous studies conducted on the lower limit of soil and its contact with saprolite layers, a great deal of work is left to standardize identification and annotation of these variables in the field. In shallow soils, the appropriately noting these limits or contacts is essential for determining their behavior and potential use. The aims of this study were to identify and define the field contact and/or transition zone between soil and saprolite in profiles of an Alisol derived from fine sandstone and siltstone/claystone in subtropical southern Brazil and to subsequently validate the field observations through a multivariate analysis of laboratory analytical data. In the six Alisol profiles evaluated, the sequence of horizons found was A, Bt, C, and Cr, where C was considered part of the soil due to its pedogenetic structure, and Cr was considered saprolite due to its rock structure. The morphological properties that were determined in the field and that were different between the B and C horizons and the Cr layer were color, structure, texture, and fragments of saprolite. According to the test of means, the properties that support the inclusion of the C horizon as part of the soil are sand, clay, water-dispersible clay, silt/clay ratio, macroporosity, total porosity, resistance to penetration, cation exchange capacity, Fe extracted by DCB, Al, H+Al, and cation exchange capacity of clay. The properties that support the C horizon as a transition zone are silt, Ca, total organic C, and Fe extracted by ammonium oxalate. Discriminant analysis indicated differences among the three horizons evaluated.

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

Reply to "Comment on 'Solutions of the telegrapher's equation in the presence of traps'"

This reply adds a number of details to remarks by Foong and Kanno [preceding Comment, Phys. Rev. A 46, 5296 (1992)] on our paper [Phys. Rev. A 45, 2222 (1992)] regarding the discontinuities observed in the curves generated in that paper.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Water tanks as ecosystems. Local ecosystemic perception for integral management of water tanks in Tamil Nadu, South India

Water tanks offer from many centuries ago solutions in South India for several problems related with water scarcity. They are a traditional water harvesting system wide spread in this territory, allowing a potential decentralized and participatory management of the local population on their own resources. Although water tanks¿ main function is irrigation, they have many other uses, functions and natural resources associated, involving stakeholders in the villages apart from those farmers making use of the irrigation. Water tanks provide a variety of landscapes and biodiversity that creates a valuable heterogeneous territory. The complexity of such an ecosystem should be managed with an integral perspective, considering all the elements involved and their relations, and understanding that water tanks are not just water deposits. This multidisciplinary study tries to demonstrate the idea of water tanks as ecosystems, describing and analyzing deeply and in an unprecedentedly way the functions, uses, natural resources and stakeholders. The research also focuses in the assessment of the ecosystemic perception of the local population of some villages in Tamil Nadu, employing diverse anthropological methodology.

Integral Bridge Abutment-to-Approach Slab Connection Final Report, June 2008

The Iowa Department of Transportation has long recognized that approach slab pavements of integral abutment bridges are prone to settlement and cracking, which manifests as the “bump at the end of the bridge”. A commonly recommended solution is to integrally attach the approach slab to the bridge abutment. Two different approach slabs, one being precast concrete and the other being cast-inplace concrete, were integrally connected to side-by-side bridges and investigated. The primary objective of this investigation was to evaluate the approach slab performance and the impacts the approach slabs have on the bridge. To satisfy the research needs, the project scope involved a literature review, survey of Midwest Department of Transportation current practices, implementing a health monitoring system on the bridge and approach slab, interpreting the data obtained during the evaluation, and conducting periodic visual inspections. Based on the information obtained from the testing the following general conclusions were made: The integral connection between the approach slabs and the bridges appear to function well with no observed distress at this location and no relative longitudinal movement measured between the two components; Tying the approach slab to the bridge appears to impact the bridge; The two different approach slabs, the longer precast slab and the shorter cast-in-place slab, appear to impact the bridge differently; The measured strains in the approach slabs indicate a force exists at the expansion joint and should be taken into consideration when designing both the approach slab and the bridge; The observed responses generally followed an annual cyclic and/or short term cyclic pattern over time.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Competitive evaporation in arrays of droplets

We consider the evaporation of periodic arrays of initially equal droplets in two-dimensional systems with open (absorbing) boundaries. Our study is based on the numerical solution of the Cahn-Hilliard equation. We show that due to cooperative effects the droplets which are further from the boundary may evaporate earlier than those in the boundary¿s vicinity. The time evolution of the overall amount of matter in the system is also studied.