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.

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

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Instrumentation and Monitoring of Precast Bridge Approach Tied to an Integral Abutment Bridge in Bremer County, SPR 0000-005, 2010

Approach slab pavement at integral abutment (I-A) bridges are prone to settlement and cracking, which has been long recognized by the Iowa Department of Transportation (DOT). A commonly recommended solution is to integrally attach the approach slab to the bridge abutment. This study sought to supplement a previous project by instrumenting, monitoring, and analyzing the behavior of an approach slab tied to a integral abutment bridge. The primary objective of this investigation was to evaluate the performance of the approach slab. To satisfy the research needs, the project scope involved reviewing a similar previous study, implementing a health monitoring system on the approach slab, interpreting the data obtained during the evaluation, and conducting periodic visual inspections of the bridge and approach slab. Based on the information obtained from the testing, the following general conclusions were made: the integral connection between the approach slab and the bridge appears to function well with no observed distress at this location and no relative longitudinal movement measured between the two components; 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 and the observed responses generally followed an annual cyclic and/or short term cyclic pattern over time; the expansion joint at one side of the approach slab does not appear to be functioning as well as elsewhere; much larger frictional forces were observed in this study compared to the previous study.

Pile Design and Tests for Integral Abutment Bridges, HR-273, 1987

Expansion joints increase both the initial cost and the maintenance cost of bridges. Integral abutment bridges provide an attractive design alternative because expansion joints are eliminated from the bridge itself. However, the piles in these bridges are subjected to horizontal movement as the bridge expands and contracts during temperature changes. The objective of this research was to develop a method of designing piles for these conditions. Separate field tests simulating a pile and a bridge girder were conducted for three loading cases: (1) vertical load only, (2) horizontal displacement of pile head only, and (3) combined horizontal displacement of pile head with subsequent vertical load. Both tests (1) and (3) reached the same ultimate vertical load, that is, the horizontal displacement had no effect on the vertical load capacity. Several model tests were conducted in sand with a scale factor of about 1:10. Experimental results from both the field and model tests were used to develop the vertical and horizontal load-displacement properties of the soil. These properties were input into the finite element computer program Integral Abutment Bridge Two-Dimensional (IAB2D), which was developed under a previous research contract. Experimental and analytical results compared well for the test cases. Two alternative design methods, both based upon the American Association of State Highway and Transportation Officials (AASHTO) Specification, were developed. Alternative One is quite conservative relative to IAB2D results and does not permit plastic redistribution of forces. Alternative Two is also conservative when compared to IAB2D, but plastic redistribution is permitted. To use Alternative Two, the pile cross section must have sufficient inelastic rotation capacity before local buckling occurs. A design example for a friction pile and an end-bearing pile illustrates both alternatives.

Validation of Design Recommendations for Integral Abutment Piles, HR-292, 1989

Since integral abutment bridges decrease the initial and maintenance costs of bridges, they provide an attractive alternative for bridge designers. The objective of this project is to develop rational and experimentally verified design recommendations for these bridges. Field testing consisted of instrumenting two bridges in Iowa to monitor air and bridge temperatures, bridge displacements, and pile strains. Core samples were also collected to determine coefficients of thermal expansion for the two bridges. Design values for the coefficient of thermal expansion of concrete are recommended, as well as revised temperature ranges for the deck and girders of steel and concrete bridges. A girder extension model is developed to predict the longitudinal bridge displacements caused by changing bridge temperatures. Abutment rotations and passive soil pressures behind the abutment were neglected. The model is subdivided into segments that have uniform temperatures, coefficients of expansion, and moduli of elasticity. Weak axis pile strains were predicted using a fixed-head model. The pile is idealized as an equivalent cantilever with a length determined by the surrounding soil conditions and pile properties. Both the girder extension model and the fixed-head model are conservative for design purposes. A longitudinal frame model is developed to account for abutment rotations. The frame model better predicts both the longitudinal displacement and weak axis pile strains than do the simpler models. A lateral frame model is presented to predict the lateral motion of skewed bridges and the associated strong axis pile strains. Full passive soil pressure is assumed on the abutment face. Two alternatives for the pile design are presented. Alternative One is the more conservative and includes thermally induced stresses. Alternative Two neglects thermally induced stresses but allows for the partial formation of plastic hinges (inelastic redistribution of forces). Ductility criteria are presented for this alternative. Both alternatives are illustrated in a design example.

Field Monitoring of Curved Girder Bridges with Integral Abutments, TPF-5(169), 2014

Nationally, there are questions regarding the design, fabrication, and erection of horizontally curved steel girder bridges due to unpredicted girder displacements, fit-up, and locked-in stresses. One reason for the concerns is that up to one-quarter of steel girder bridges are being designed with horizontal curvature. There is also an urgent need to reduce bridge maintenance costs by eliminating or reducing deck joints, which can be achieved by expanding the use of integral abutments to include curved girder bridges. However, the behavior of horizontally curved bridges with integral abutments during thermal loading is not well known nor understood. The purpose of this study was to investigate the behavior of horizontal curved bridges with integral abutment (IAB) and semi-integral abutment bridges (SIAB) with a specific interest in the response to changing temperatures. The long-term objective of this effort is to establish guidelines for the use of integral abutments with curved girder bridges. The primary objective of this work was to monitor and evaluate the behavior of six in-service, horizontally curved, steel-girder bridges with integral and semi-integral abutments. In addition, the influence of bridge curvature, skew and pier bearing (expansion and fixed) were also part of the study. Two monitoring systems were designed and applied to a set of four horizontally curved bridges and two straight bridges at the northeast corner of Des Moines, Iowa—one system for measuring strains and movement under long term thermal changes and one system for measuring the behavior under short term, controlled live loading. A finite element model was developed and validated against the measured strains. The model was then used to investigate the sensitivity of design calculations to curvature, skew and pier joint conditions. The general conclusions were as follows: (1) There were no measurable differences in the behavior of the horizontally curved bridges and straight bridges studied in this work under thermal effects. For preliminary member sizing of curved bridges, thermal stresses and movements in a straight bridge of the same length are a reasonable first approximation. (2) Thermal strains in integral abutment and semi-integral abutment bridges were not noticeably different. The choice between IAB and SIAB should be based on life – cycle costs (e.g., construction and maintenance). (3) An expansion bearing pier reduces the thermal stresses in the girders of the straight bridge but does not appear to reduce the stresses in the girders of the curved bridge. (4) An analysis of the bridges predicted a substantial total stress (sum of the vertical bending stress, the lateral bending stress, and the axial stress) up to 3 ksi due to temperature effects. (5) For the one curved integral abutment bridge studied at length, the stresses in the girders significantly vary with changes in skew and curvature. With a 10⁰ skew and 0.06 radians arc span length to radius ratio, the curved and skew integral abutment bridges can be designed as a straight bridge if an error in estimation of the stresses of 10% is acceptable.