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Los, V. F., and M. V. Los. "An Exact Solution of the Time-Dependent Schrödinger Equation with a Rectangular Potential for Real and Imaginary Times." Ukrainian Journal of Physics 61, no. 4 (April 2016): 331–41. http://dx.doi.org/10.15407/ujpe61.04.0331.
López, L. A., Omar Pedraza, and V. E. Ceron. "Time-dependent solution from Myers–Perry." Canadian Journal of Physics 94, no. 2 (February 2016): 177–79. http://dx.doi.org/10.1139/cjp-2015-0354.
We present a three-parameter time-dependent solution of the vacuum Einstein equations in five dimensions. The solution is obtained by applying the Wick rotation to the Myers–Perry solution that represents a rotating black hole in five dimensions. The new interpretation of the Myers–Perry solution can be considered among the generalized Einstein–Rosen type that can be interpreted as plane-symmetric waves, cylindrical waves or cosmological space–time in five dimensions. In some limits the solution has boost-rotational symmetry and it is asymptotically flat. In the case that the solution represents a cylindrical space–time, the E-energy is analyzed.
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Vidal, Thibaut, Rafael Martinelli, Tuan Anh Pham, and Minh Hoàng Hà. "Arc Routing with Time-Dependent Travel Times and Paths." Transportation Science 55, no. 3 (May 2021): 706–24. http://dx.doi.org/10.1287/trsc.2020.1035.
Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, and heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules, and completion bounds to find optimal solutions for problems counting up to 75 services. From these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.
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Vardy, Alan E., and James M. B. Brown. "Laminar pipe flow with time-dependent viscosity." Journal of Hydroinformatics 13, no. 4 (October 1, 2010): 729–40. http://dx.doi.org/10.2166/hydro.2010.073.
A general solution is obtained for laminar flow in axisymmetric pipes, allowing for prescribed timedependent viscosity and time-dependent pressure gradients. In both cases, the only restriction on the prescribed time dependence is that it must vary continuously; it is not necessary for rates of change to be continuous. The general solution is obtained using the Finite Hankel Transform method. This makes it possible to allow explicitly for time-dependent viscosity, but it does not permit the spatial dependence of viscosity. This contrasts with Laplace transforms, which allow spatial, but not general, temporal variations. The general solution is used to study a selection of particular flows chosen to illustrate distinct forms of physical behaviour and to demonstrate the ease with which solutions are obtained. The methodology is also applied to the simple case of constant (Newtonian) viscosity. In this case, it yields the same solutions as previously published methods, but it does so in a much simpler manner.
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MEYLAN, MICHAEL H. "Spectral solution of time-dependent shallow water hydroelasticity." Journal of Fluid Mechanics 454 (March 10, 2002): 387–402. http://dx.doi.org/10.1017/s0022112001007273.
The spectral theory of a thin plate floating on shallow water is derived and used to solve the time-dependent motion. This theory is based on an energy inner product in which the evolution operator becomes unitary. Two solution methods are presented. In the first, the solution is expanded in the eigenfunctions of a self-adjoint operator, which are the incoming wave solutions for a single frequency. In the second, the scattering theory of Lax–Phillips is used. The Lax–Phillips scattering solution is suitable for calculating only the free motion of the plate. However, it determines the modes of vibration of the plate–water system. These modes, which both oscillate and decay, are found by a complex search algorithm based contour integration. As well as an application to modelling floating runways, the spectral theory for a floating thin plate on shallow water is a solvable model for more complicated hydroelastic systems.
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Li, Nan, and Shripad Tuljapurkar. "The solution of time‐dependent population models." Mathematical Population Studies 7, no. 4 (January 2000): 311–29. http://dx.doi.org/10.1080/08898480009525464.
Evans, D. J., and A. A. Al-kharafi. "Finite element solution of time-dependent problems." International Journal of Computer Mathematics 22, no. 3-4 (January 1987): 287–302. http://dx.doi.org/10.1080/00207168708803599.
Paasschens, J. C. J. "Solution of the time-dependent Boltzmann equation." Physical Review E 56, no. 1 (July 1, 1997): 1135–41. http://dx.doi.org/10.1103/physreve.56.1135.
Abdou, M. A. "On the solution of time-dependent problems." Journal of Quantitative Spectroscopy and Radiative Transfer 95, no. 2 (October 2005): 271–84. http://dx.doi.org/10.1016/j.jqsrt.2004.08.044.
An efficient, accurate and reliable numerical solver is essential for solving complex mathematical models and obtaining their computational approximations. The solver presented in this work is built upon nonlinear multigrid with the full approximation scheme (FAS). Its implementation is achieved, in part, using a complex, open source software library PARAMESH, and the resulting numerical solver, Campfire, also combines with adaptive mesh refinement, adaptive time stepping and parallelization through domain decomposition. There are five mathematical models considered in this work, ranging from applications such as binary alloy solidification and fluid dynamics to a multi-phase-field model of tumour growth. These mathematical models consist of nonlinear, time-dependent and coupled partial differential equations (PDEs). Using our adaptive, parallel multigrid solver, together with finite difference method (FDM) and backward differentiation formulas (BDF), we are able to solve all five models in computationally demanding 2-D and/or 3-D situations. Due to the choice of second order central finite difference and second order BDF2 method, we obtain, and demonstrate, solutions with an overall second order convergence rate and optimal multigrid convergence. In the case of the multi-phase-field model of tumour growth, this has not previously been achieved. The novelties of our work also include solving the model of binary alloy solidification with a time-dependent temperature field in 3-D for the first time; implementing non-time-dependent equations alongside the coupled time-dependent partial differential equations (and increasing the range of boundary conditions) to significantly increase the generality and range of applicability of the described multigrid solver; improving the efficiency of the implementation of the solver through multiple developments; and introducing penalty terms to smoothly control the behaviour of phase variables where their range of valid values is constrained.
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McDonald, Eleanor. "All-at-once solution of time-dependent PDE problems." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:60f2985b-6071-47ae-97a9-7813db0194ae.
In this thesis, we examine the solution to a range of time-dependent Partial Differential Equation (PDE) problems. Throughout, we focus on the development of preconditioners for the all-at-once system, which solves for all time-steps in a single coupled computation. The preconditioners developed are used with existing iterative methods and, due to their specific block structure, could be applied in parallel over time. We first develop solvers for the heat equation and the transient convection-diffusion equation. For both of these forward problems, the all-at-once system is non-symmetric. Despite this, in certain cases, we are able to provide rigorous termination bounds for non-symmetric iterative methods, contrary to what is generally possible for non-symmetric systems. The ideas developed for evolutionary PDEs are extended to develop preconditioners for time-dependent optimal control problems. By incorporating the methods designed for the forward problem, we are able to develop block diagonal Schur complement based preconditioners, which also could be implemented in parallel over time. We provide extensive eigenvalue analysis for each preconditioner and demonstrate their effectiveness through numerical computations for a variety of problems. We are able to describe solvers that are robust to various parameters, including the mesh size and number of time-steps.
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Tråsdahl, Øystein. "Numerical solution of partial differential equations in time-dependent domains." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9752.
Numerical solution of heat transfer and fluid flow problems in two spatial dimensions is studied. An arbitrary Lagrangian-Eulerian (ALE) formulation of the governing equations is applied to handle time-dependent geometries. A Legendre spectral method is used for the spatial discretization, and the temporal discretization is done with a semi-implicit multi-step method. The Stefan problem, a convection-diffusion boundary value problem modeling phase transition, makes for some interesting model problems. One problem is solved numerically to obtain first, second and third order convergence in time, and another numerical example is used to illustrate the difficulties that may arise with distribution of computational grid points in moving boundary problems. Strategies to maintain a favorable grid configuration for some particular geometries are presented. The Navier-Stokes equations are more complex and introduce new challenges not encountered in the convection-diffusion problems. They are studied in detail by considering different simplifications. Some numerical examples in static domains are presented to verify exponential convergence in space and second order convergence in time. A preconditioning technique for the unsteady Stokes problem with Dirichlet boundary conditions is presented and tested numerically. Free surface conditions are then introduced and studied numerically in a model of a droplet. The fluid is modeled first as Stokes flow, then Navier-Stokes flow, and the difference in the models is clearly visible in the numerical results. Finally, an interesting problem with non-constant surface tension is studied numerically.
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Abd, El Aziz Osama Mostafa. "Solution of time dependent problems using the Global Element Method." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329416.
Johansson, Karoline. "A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1082.
Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. This theorem was proved by choosing $$\widehat{f}(\xi )=\widehat{f_a}(\xi )= | \xi | ^{-n} (\log | \xi |)^{-3/4} \sum_{j=1}^{\infty} \chi _j(\xi)e^{- i( x_{n_j} \cdot \xi + t_j | \xi | ^a)}, \, a=2,$$ where $\chi_j$ is the characteristic function of shells $S_j$ with the inner radius rapidly increasing with respect to $j$. The purpose of this essay is to explain the proof given by Sjögren and Sjölin, by first showing that the theorem is true for $\gamma (t)=t$, and to investigate the result when we use $$S^a f_a (x, t)= (2 \pi)^{-n}\int_{\RR} {e^{i x\cdot \xi}e^{it |\xi|^a}\widehat{f_a}(\xi)}\, d \xi$$ instead of $u$.
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Loskutov, Valentin, and Vyacheslav Sevriugin. "Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-194287.
The purpose of our work is to attempt to find the analytical expression approximating the experimentally obtained D(t) dependence of molecules of liquids or gases, in porous systems. The statement of the problem is based on the most general representations of self-diffusion processes in porous systems.
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Loskutov, Valentin, and Vyacheslav Sevriugin. "Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium." Diffusion fundamentals 5 (2007) 3, S. 1-5, 2007. https://ul.qucosa.de/id/qucosa%3A14267.
The purpose of our work is to attempt to find the analytical expression approximating the experimentally obtained D(t) dependence of molecules of liquids or gases, in porous systems. The statement of the problem is based on the most general representations of self-diffusion processes in porous systems.
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Stoor, Daniel. "Solution of the Stefan problem with general time-dependent boundary conditions using a random walk method." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-385147.
This work deals with the one-dimensional Stefan problem with a general time- dependent boundary condition at the fixed boundary. The solution will be obtained using a discrete random walk method and the results will be compared qualitatively with analytical- and finite difference method solutions. A critical part has been to model the moving boundary with the random walk method. The results show that the random walk method is competitive in relation to the finite difference method and has its advantages in generality and low effort to implement. The finite difference method has, on the other hand, higher accuracy for the same computational time with the here chosen step lengths. For the random walk method to increase the accuracy, longer execution times are required, but since the method is generally easily adapted for parallel computing, it is possible to speed up. Regarding applications for the Stefan problem, there are a large range of examples such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for oil extraction using steam assisted gravity drainage.
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Schroeder, Gregory C. "Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17404.
Bibliography: pages 93-101. The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory.
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Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.
In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis.
Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear' s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.
Hundsdorfer, Willem, and Jan Verwer. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-09017-6.
Eliasson, Peter. A solution method for the time-dependent Navier-Stokes equations for laminar, incompressible flow. Stockholm: Aeronautical Research Institute of Sweden, 1989.
Baumeister, Kenneth J. Time-dependent parabolic finite difference formulation for harmonic sound propagation in a two-dimensional duct with flow. [Washington, D.C: National Aeronautics and Space Administration, 1996.
Baumeister, Kenneth J. Time-dependent parabolic finite difference formulation for harmonic sound propagation in a two-dimensional duct with flow. [Washington, D.C: National Aeronautics and Space Administration, 1996.
Harper, Pat. The natural solution to diabetes: [lower your blood sugar 25% simply, safely, without drugs : lose weight, beat your disease--one step at a time]. Pleasantville, N.Y: Reader's Digest, 2004.
Book chapters on the topic "Time dependent solution":
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Peterson, James K. "The Time Dependent Cable Solution." In BioInformation Processing, 45–58. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-287-871-7_4.
de Boeij, P. L. "Solution of the Linear-Response Equations in a Basis Set." In Time-Dependent Density Functional Theory, 211–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-35426-3_13.
Mansur, W. J., and C. A. Brebbia. "Further Developments on the Solution of the Transient Scalar Wave Equation." In Time-dependent and Vibration Problems, 87–123. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-29651-6_4.
Mansur, W. J., and C. A. Brebbia. "Further Developments on the Solution of the Transient Scalar Wave Equation." In Time-dependent and Vibration Problems, 87–123. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82398-5_4.
Hundsdorfer, Willem, and Jan Verwer. "Time Integration Methods." In Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, 139–214. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-09017-6_2.
Hohlov, Y. E. "Explicit Solution of Time-Dependent Free Boundary Problems." In Free Boundary Problems in Continuum Mechanics, 131–40. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8627-7_15.
Conference papers on the topic "Time dependent solution":
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Rizea, M. "On the Numerical Solution of the Time‐Dependent Schrödinger Equation with Time‐Dependent Potentials." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990863.
Wong, Bernardine Renaldo, Swee-Ping Chia, Kurunathan Ratnavelu, and Muhamad Rasat Muhamad. "Numerical Solution Of The Time-Dependent Schrödinger equation." In FRONTIERS IN PHYSICS: 3rd International Meeting. AIP, 2009. http://dx.doi.org/10.1063/1.3192278.
Liu, Pingyu, and Robert A. Kruger. "Solution to the time-dependent photon transport equation." In Europto Biomedical Optics '93, edited by Martin J. C. van Gemert, Rudolf W. Steiner, Lars O. Svaasand, and Hansjoerg Albrecht. SPIE, 1994. http://dx.doi.org/10.1117/12.168023.
Kiss, G. Zs, S. Borbély, and L. Nagy. "Momentum space iterative solution of the time-dependent Schrödinger equation." In TIM 2012 PHYSICS CONFERENCE. AIP, 2013. http://dx.doi.org/10.1063/1.4832799.
Meylan, Michael H. "Time-Dependent Solution for Linear Water Waves by Expansion in the Single-Frequency Solutions." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57048.
We consider the solution in the time-domain of water wave scattering by fixed bodies (which may or may not intersect with the free surface). We show how the the problem with arbitrary initial conditions can be found using the single-frequency solutions. This result relies on a special inner product and is known as a generalized eigenfunction expansion (because the operator has a continuous spectrum). We also show how this expansion should be modified when trapped modes are present.
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Majdalani, J., W. Van Moorhem, J. Majdalani, and W. Van Moorhem. "An improved time-dependent flowfield solution for solid rocket motors." In 33rd Joint Propulsion Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-2717.
Pindzola, M. S., and P. Gavras. "Direct solution of the time-dependent Schrödinger equation for atomic processes." In Atomic collisions: A symposium in honor of Christopher Bottcher (1945−1993). AIP, 1995. http://dx.doi.org/10.1063/1.49197.
Hong, Lianxi, and Min Xu. "A Model of MDVRPTW with Fuzzy Travel Time and Time-Dependent and Its Solution." In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2008. http://dx.doi.org/10.1109/fskd.2008.77.
Subbarayalu, Sethuramalingam, and Lonny L. Thompson. "HP-Adaptive Time-Discontinuous Galerkin Finite Element Methods for Time-Dependent Waves." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60403.
hp-Adaptive time-discontinuous Galerkin methods are developed for second-order hyperbolic systems. Explicit a priori error estimates in terms of time-step size, approximation order, and solution regularity are derived. Knowledge of these a priori convergence rates in combination with a posteriori error estimates computed from the jump in time-discontinuous solutions are used to automatically select time-step size h and approximation order p to achieve a specified error tolerance with a minimal number of total degrees-of-freedom. We show that the temporal jump error is a good indicator of the local error, and the summation of jump error for the total interval is good indicator for the global and accumulation errors. In addition, the accumulation error at the end of a time-step can be estimated well by the summation of the local jump error at the beginning of a time-step provided the approximation order is greater or equal to the solution regularity. Superconvergence of the end points of a time-step for high-order polynomials are also demonstrated.
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Su, Qichang C., S. Mandel, S. Menon, and R. Grobe. "Split operator solution of the time-dependent Maxwell's equations for random scatterers." In International Workshop on Photonics and Imaging in Biology and Medicine, edited by Qingming Luo, Britton Chance, and Valery V. Tuchin. SPIE, 2002. http://dx.doi.org/10.1117/12.462558.
Mish, Kyran D., and Leonard R. Herrmann. The Solution of Large Time-Dependent Problems Using Reduced Coordinates. Fort Belvoir, VA: Defense Technical Information Center, June 1987. http://dx.doi.org/10.21236/ada182618.
Oliger, Joseph. Computing Methods for the Approximate Solution of Time Dependent Problems. Fort Belvoir, VA: Defense Technical Information Center, November 1994. http://dx.doi.org/10.21236/ada286007.
Mish, Kyran D., Darl M. Romstad, and Leonard R. Herrmann. The Solution of Nonlinear Time-Dependent Problems Usng Modal Coordinates. Fort Belvoir, VA: Defense Technical Information Center, December 1985. http://dx.doi.org/10.21236/ada163535.
Yeon, Kyu H., Thomas F. George, and Chung I. Um. Exact Solution of a Quantum Forced Time-Dependent Harmonic Oscillator. Fort Belvoir, VA: Defense Technical Information Center, June 1991. http://dx.doi.org/10.21236/ada236633.
Draganescu, Andrei. Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report). Office of Scientific and Technical Information (OSTI), February 2019. http://dx.doi.org/10.2172/1494701.
Figliozzi, Miguel. Freight Distribution Problems in Congested Urban Areas: Fast and Effective Solution Procedures to Time-Dependent Vehicle Routing Problems. Portland State University Library, January 2011. http://dx.doi.org/10.15760/trec.108.
Rojas-Bernal, Alejandro, and Mauricio Villamizar-Villegas. Pricing the exotic: Path-dependent American options with stochastic barriers. Banco de la República de Colombia, March 2021. http://dx.doi.org/10.32468/be.1156.
We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.
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Coskun, E., and M. K. Kwong. Parallel solution of the time-dependent Ginzburg-Landau equations and other experiences using BlockComm-Chameleon and PCN on the IBM SP, Intel iPSC/860, and clusters of workstations. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/266722.
Graber, Ellen R., Linda S. Lee, and M. Borisover. An Inquiry into the Phenomenon of Enhanced Transport of Pesticides Caused by Effluents. United States Department of Agriculture, July 1995. http://dx.doi.org/10.32747/1995.7570559.bard.
The objective of this collaborative research project was to determine the factors that may cause enhanced pesticide transport under effluent irrigation. For s-triazines, the potential for enhanced transport through association with effluent dissolved organic matter (OM) was shown to be small in batch and column studies and in numerical simulations. High alkalinity and pH of treated effluents increased soil-solution pH for selected soil-effluent combinations, promoting the dissolution of soil OM and mobilizing otherwise OM-retained pesticides. Evapotranspiration in column studies resulted in increased pore-water concentrations of dissolved OM and some pesticide transport enhancement with the greatest effect observed with OM-poor soils. For ionogenic pesticides, effluent-induced increases in soil-solution pH increased the mobility of pesticides with acid dissociation constants within 2 pH units of the initial soil-solution pH. Effluents high in suspended solids and/or monovalent cations resulted in blockage of soil pores reducing water-flow velocity and/or changing flow paths. Reduced flow resulted in an increase in desorption time of soil sorbed pesticides, increasing the amount available for further transport with the net effect being soil texture dependent. In terms of pesticide degradation in soils, effluents appeared to have only a minor effect for the few pesticides investigated.
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Hong Qin and Ronald C. Davidson. Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field. Office of Scientific and Technical Information (OSTI), July 2011. http://dx.doi.org/10.2172/1029998.
