Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Rachel Kuske is active.

Publication


Featured researches published by Rachel Kuske.


Applied Mathematical Finance | 1998

Optimal exercise boundary for an American put option

Rachel Kuske; Joseph B. Keller

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Greens theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic solution is the result of Barles et al. An asymptotic solution for the option price is obtained also.


Journal of Applied Mechanics | 2007

An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case

Sarah L. Mitchell; Rachel Kuske; Anthony Peirce

This paper presents a novel asymptotic framework to obtain detailed solutions describing the propagation of hydraulic fractures in an elastic material. The problem consists of a system of nonlinear integro-differential equations and a free boundary problem. This combination of local and nonlocal effects leads to transitions on a small scale near the crack tip, which control the behavior across the whole fracture profile. These transitions depend upon the dominant physical process(es) and are identified by simultaneously scaling the associated parameters with the distance from the tip. A smooth analytic solution incorporating several physical processes in the crucial tip region can be constructed using this new framework. In order to clarify the exposition of the new methodology, this paper is confined to considering the impermeable case in which only the two physical processes of viscous dissipation and structure energy release compete.


Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences | 2001

Asymptotics of cellular buckling close to the Maxwell load

C. J. Budd; G. W. Hunt; Rachel Kuske

We study the deformation of an elastic strut on a nonlinear Winkler foundation subjected to an axial compressive load P. Using multi–scale analysis and numerical methods we describe the localized, cellular, post–buckled state of the system when P is removed from the critical load P = 2. The solutions, and their modulation frequencies, differ significantly from those predicted by weakly nonlinear analysis very close to P = 2. In particular, when P approaches the Maxwell load PM , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of PM in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.


Journal of Computational Physics | 1990

A two-dimensional adaptive pseudo-spectral method

A. Bayliss; Rachel Kuske; B. J. Matkowsky

We develop a two-dimensional adaptive pseudo-spectral procedure which is capable of improving the approximation of functions which are rapidly varying in two dimensions. The method is based on introducing two-dimensional coordinate transformations chosen to minimize certain functionals of the solution to be approximated. The method is illustrated by numerical computation of the solutions to a system of reaction diffusion equations modeling the gasless combustion of a solid fuel. Spatio-temporal patterns are computed as a parameter μ, related to the activation energy, is increased above a critical value μc. The spatial patterns are characterized by a very rapid variation in the direction of the axis of the cylinder, together with a standing wave pattern in the direction of the azimuthal angle ψ For small values of μ − μc the solutions exhibit a nearly sinusoidal dependence in both time and ψ As μ is increased further relaxation oscillations in both time and ψ occur. Beyond a critical value of μ stable time-periodic solutions are no longer found and the solution exhibits a quasi-periodic time dependence.


Biophysical Journal | 2008

Direct observation of markovian behavior of the mechanical unfolding of individual proteins.

Yi Cao; Rachel Kuske; Hongbin Li

Single-molecule force-clamp spectroscopy is a valuable tool to analyze unfolding kinetics of proteins. Previous force-clamp spectroscopy experiments have demonstrated that the mechanical unfolding of ubiquitin deviates from the generally assumed Markovian behavior and involves the features of glassy dynamics. Here we use single molecule force-clamp spectroscopy to study the unfolding kinetics of a computationally designed fast-folding mutant of the small protein GB1, which shares a similar beta-grasp fold as ubiquitin. By treating the mechanical unfolding of polyproteins as the superposition of multiple identical Poisson processes, we developed a simple stochastic analysis approach to analyze the dwell time distribution of individual unfolding events in polyprotein unfolding trajectories. Our results unambiguously demonstrate that the mechanical unfolding of NuG2 fulfills all criteria of a memoryless Markovian process. This result, in contrast with the complex mechanical unfolding behaviors observed for ubiquitin, serves as a direct experimental demonstration of the Markovian behavior for the mechanical unfolding of a protein and reveals the complexity of the unfolding dynamics among structurally similar proteins. Furthermore, we extended our method into a robust and efficient pseudo-dwell-time analysis method, which allows one to make full use of all the unfolding events obtained in force-clamp experiments without categorizing the unfolding events. This method enabled us to measure the key parameters characterizing the mechanical unfolding energy landscape of NuG2 with improved precision. We anticipate that the methods demonstrated here will find broad applications in single-molecule force-clamp spectroscopy studies for a wide range of proteins.


Physica D: Nonlinear Phenomena | 2011

Mixed-mode oscillations in a stochastic, piecewise-linear system

David J. W. Simpson; Rachel Kuske

Abstract We analyse a piecewise-linear FitzHugh–Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity of the canard point. We determine the effect of each model parameter on the stochastically driven MMOs. In particular we show that any parameter variation (such as a modification of the piecewise-linear function in the model) that leaves the ratio of noise amplitude to time-scale separation unchanged typically has little effect on the width of the interval of the primary bifurcation parameter over which MMOs occur. In that sense, the MMOs are robust. Furthermore, we show that the piecewise-linear model exhibits MMOs more readily than the classical FitzHugh–Nagumo model for which a cubic polynomial is the only nonlinearity. By studying a piecewise-linear model, we are able to explain results using analytical expressions and compare these with numerical investigations.


Siam Journal on Applied Mathematics | 2007

An Asymptotic Framework for Finite Hydraulic Fractures Including Leak‐Off

Sarah L. Mitchell; Rachel Kuske; Anthony Peirce

The dynamics of hydraulic fracture, described by a system of nonlinear integro- differential equations, is studied through the development and application of a multiparameter sin- gular perturbation analysis. We present a new single expansion framework which describes the interaction between several physical processes, namely viscosity, toughness, and leak-off. The prob- lem has nonlocal and nonlinear effects which give a complex solution structure involving transitions on small scales near the tip of the fracture. Detailed solutions obtained in the crack tip region vary with the dominant physical processes. The parameters quantifying these processes can be identi- fied from critical scaling relationships, which are then used to construct a smooth solution for the fracture depending on all three processes. Our work focuses on plane strain hydraulic fractures on long time scales, and this methodology shows promise for related models with additional time scales, fluid lag, or different geometries, such as radial (penny-shaped) fractures and the classical Perkins-Kern-Nordgren (PKN) model. 1. Introduction. Hydraulic fractures are propagated in an elastic material due to the pressure exerted by a viscous fluid on the fracture. These fractures occur nat- urally in volcanic dikes where magma causes fracture propagation below the surface of the earth (37, 38, 55). In the oil and gas industry hydraulic fractures are deliber- ately propagated in reservoirs to increase production. Hydraulic fracture models need to account for the primary physical mechanisms involved: deformation of the rock, fracturing of the rock, flow of viscous fluid within the fracture, and leak-off of the fracturing fluid into the permeable rock. The parameters that characterize these pro- cesses are, respectively, Youngs modulus E and Poissons ratio ν, the rock toughness KIc, the fluid viscosity μ, and the leak-off coefficient Cl. The challenges for analysis of these models originate from the nonlinearity of the equation describing the flow of fluid in the fracture, the nonlocal character of the elas- tic response of the fracture, and the history-dependence of the equation governing the exchange of fluid between the fracture and the rock. The singular tip behavior, which can be difficult to resolve numerically, dominates these solutions and is highly depen- dent on the relative importance of the contributing physical processes. Therefore, the objectives of analytic treatment of these models are as follows: to characterize the structure of the near-tip solution that can be embedded in numerical algorithms, to provide benchmark solutions to test numerical codes, and to determine the parameter values and length scales that characterize the transitions between distinct combina- tions of physical processes. In this paper we use a novel asymptotic framework that enables us to characterize the different propagation regimes and provide asymptotic solutions when more than two physical processes are competing simultaneously. This


Journal of Statistical Physics | 1999

Probability Densities for Noisy Delay Bifurcations

Rachel Kuske

The delay of a transition in a nonlinear system due to a slowly varying control parameter can be significantly reduced by very small noise. A new asymptotic approximation for the time-dependent probability density function gives a complete description of the process into the transition region, and is easily interpreted in terms of the noisy dynamics. It is also used to calculate mean transition times. The method is applied to two nonlinear systems with noise: a one-dimensional canonical model for a steady bifurcation and the noisy FitzHugh–Nagumo model.


Optics Communications | 1997

Localized synchronization of two coupled solid state lasers

Rachel Kuske; Thomas Erneux

Abstract Two coupled lasers exhibiting oscillatory intensities are known to synchronize in phase or out-of-phase and with equal intensities. But a different form of synchronization - called localization - has been discussed recently in the literature of coupled oscillators. Localization means that the two lasers may exhibit different intensities. We show that this phenomenon is possible in a system of two coupled solid state lasers differing only by their detunings. We determine the bifurcation diagram of the localized states and obtain analytical conditions for stable localization.


Multiscale Modeling & Simulation | 2005

Multiscale Analysis of Stochastic Delay Differential Equations

Malgorzta M. Klosek; Rachel Kuske

We apply multiscale analysis to stochastic delay differential equations, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays of deterministic ...

Collaboration


Dive into the Rachel Kuske's collaboration.

Top Co-Authors

Avatar
Top Co-Authors

Avatar

Yue-Xian Li

University of British Columbia

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Yue Xian Li

University of British Columbia

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Tony Shardlow

University of Manchester

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Salah-Eldin A. Mohammed

Southern Illinois University Carbondale

View shared research outputs
Top Co-Authors

Avatar

Thomas Erneux

Université libre de Bruxelles

View shared research outputs
Researchain Logo
Decentralizing Knowledge