Numerical analysis and scientific computation

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial "positive alpha." As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with basic knowledge of markets and finance can readily understand. To address my first goal a well-quoted and tradable asset was required. To create a model that traders can use to make money it needed to be volatile with significant short and longer-term price swings. After some analysis, a review of macroeconomic impacts, and drawing in some part on experience, oil emerged as a fitting test, in particular Brent Crude Oil. For simplicity, and to further my third goal, "Oil" as used within this paper will represent Brent Crude Oil unless otherwise specified. While some dissertations and other scholarly works set out to discern theoretical truths this dissertation is much simpler, this is all about the money. Though I am certainly interested, as I am sure many traders are, in discovering the "Holy Grail" of how to trade any type of asset, the scope of my analysis will be confined to Brent Crude Oil prices within a sampling period of January 2002 thru May 2016. The findings indicate that there are factors that are predictive of Table of Contents Abstract .

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model were used in combination with an airplane polynomial drag model to estimate important performance speeds. Except for the airframe-only dependent control airspeeds, all performance speeds are airframepowerplant dependent. In all analytical considerations one ends up with polynomials of the 4 th order that have no closed-form solutions. A real positive-root seeking numerical procedure based on the family of Newton-Raphson methods was used to extract performance airspeeds for variable in-flight weights and altitudes in the ISA troposphere. Extensive testing of the accuracy and convergence of the Newton-Raphson nonlinear equation solvers was conducted before performance speed calculations. A fictitious long-range wide-body transport-category airplane was modeled in combination with a pair of high-bypass and ultra-high bypass ratio flat-rated turbofans. Procedure employed here can be easily extended to cases when fitted, measured drag and thrust data is given in arbitrary polynomial forms. Sensitivity analysis is performed on minimum-drag airspeed and maximum aerodynamic efficiency. Transonic wave drag considerations are introduced.

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane's bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment may already be a part of other lateral-directional stability derivatives, most probably in dihedral effect. Nevertheless, the overbanking tendency may also be induced by propulsive and/or gyroscopic moments, airplane and flight control rigging problems, human factors, and improper piloting techniques. Straightforward explanation of the overbanking tendency is based on the asymptotic spiral divergence lateral-directional mode, which is very common in many FAR 23 airplane designs. The full nonlinear stability model, which may include coupling of longitudinal, lateral, and directional motion in steep turns at high angles of attack and including propulsive moments, may be required to make the final judgment about the existence of the overbanking tendency. A thorough review of airplane turning performance in horizontal plane is presented.

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The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualization, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.

The recent study from one of our collaborator students showed the effect of curcumin on the MCF-7 breast cancer cell and its ability to inhibit the growth-inducing caspase-mediated apoptosis of cell via the MAPK pathway. Based on this study we compared two mathematical models (Bertalanffy and Gompertz) that would be best fits to the data from the experiments of the MCF-7 breast cancer cell study. To find the best model, in the outside we used Powel method to solve the ordinary differential equation (ODE)-based optimization, where the objective is to minimize the sum of square errors (SSE) which are the differences between the data points and the models. In the inside we used Runge Katta method to solve the ODEs. We also used other statistics measurements, which are Akaike information criterion (AIC) and Bayesian information criterion (BIC). Based on the three measurements we found that the best fit model is the Gompertz. Additionally, we could see the best model from the graphs of the models and the data points. Our results also had good agreements with the previous studies on the modeling of the MCF-7 breast cancer cell that the Gompertz is the best fit model for the breast cancer.

Our work addresses two important issues with recurrent neural networks: (1) they are overparametrized, and (2) the recurrent weight matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.

It is well known that the set of Mahler measures of single variable polynomial has limit points of which a list established by D. Boyd and M. Mossinghoff has been extended through approaches based on genetic algorithms. In this paper, we wish to further extend the list of known limit points by adapting a method of missing data restoration.

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et al. [Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes, J. Comput. Phys. ( )], to a fully-coupled, provably second-order accurate scheme in time, while maintaining energy-stability. The new method requires fewer matrix assemblies in each Newton iteration resulting in faster solution time. The method is based on a fully-implicit Crank-Nicolson scheme in time and a pressure stabilization for an equal order Galerkin formulation. That is, we use a conforming continuous Galerkin (cG) finite element method in space equipped with a residualbased variational multiscale (RBVMS) procedure to stabilize the pressure. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise, Rayleigh-Taylor instability, and lid-driven cavity flow problems. We analyze in detail the scaling of our numerical implementation.

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler-Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.

With the help of some standard results in Geometry, Differential geometry, Spherical Trigonometry and the latitude and longitude of two places on the surface of the earth one can measure the Geodesics of the path joining those places and the direction between two places with respect to the geographical position. The study of geodesics on a sphere aroses in connection with geodesy specially with the solution of triangulation networks. The figure of the earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. Instead of finding networks as a two dimensional problem, these problems are now solved by three dimensional methods. The main objectives of this paper is to find the distances and directions of the sum of different renowned places named Dhaka to Mecca, London to Mecca, NewYork to Mecca and Delhi to Mecca with the help of the knowledge of differential geometry.

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM, while CIVA has a 2D FEM solver [1-3]. In this work, we study the performance of the Nyström method (NM) [4,5], an alternative boundary integral equation solver to the BEM, in modeling ultrasonic scattering from defects. To handle larger problems, the Nyström method is accelerated by...

As we approach solar convection simulations that seek to model the interaction of small-scale granulation and supergranulation and even larger scales of convection within the near-surface shear layer (NSSL), the treatment of the boundary conditions and minimization of sub-grid scale diffusive processes become increasingly crucial. We here assess changes in the dynamics and the energy flux balance of the flows established in rotating spherical shell segments that capture much of the NSSL with the Curved Spherical Segment (CSS) code using two different diffusion schemes. The CSS code is a new massively parallel modeling tool capable of simulating 3-D compressible MHD convection with a realistic solar stratification in rotating spherical shell segments.

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler-Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.

This study tries to analyze the reasons for the downturn of the carpet weaving industry in the Golestan Province and also takes advantage of experts' opinions and viewpoints. The Q methodology was used to achieve a comprehensive understanding of the causes of the downturn. A total of 26 experts of the Turkmen hand-woven carpet were selected for conducting "Q-sort" data collection procedure. The fac� tor analysis was conducted through a heuristic method using correlation matrix in order to identify the participant's mental paradigms (viewpoints). Finally, six factors or viewpoints, with the total variance of 86.7, were identified. A total of 16 statements were offered in this regard including the following state� ments: 1) Lack of innovation and creativity and marketing problems; 2) Technical and technological back� wardness and low economic proficiency; 3) Expensive cost of raw materials, lack of innovation; 4) The changed lifestyle and understanding carpet weaving as a hard work; 5) The weak planning system and institutional inefficiency; and 6) Lack of motivation, changed livelihood, and low economic proficiency. The results indicate that the statement 3 has the highest score (with the factor score of 2.05) among the various statements. This statement is followed by youth, especially young rural girls, unwillingness to work in carpet weaving field and learning its skills (score: 1.93) and lack of innovation and creativity in designs, colors, motifs and quality of the raw materials to improve the quality of carpets (score: 1.93).

The present special issue is yet one more collective endeavor in the area of educational research that demonstrates how the new science of complex dynamical systems could be applied in this domain. In social sciences, while the linear methodologies are, at the moment still the main stream, the appreciation of the new paradigm has already been growing, and a considerable body of research has been published recently in regular journals, special issues on complexity and edited book volumes. In physiology, behavioral sciences, economics and life sciences, complexity theory and nonlinear dynamics have been proven highly influential advancing the discipline. Education is no longer a late follower to those developments, but a privileged area where complex dynamical system (CDS) is by now an established paradigm. Complexity theory has inspired researchers and scholars working in education and curriculum studies to approach their subject matter from a different angle, and ask different quest...

Literature on educational reforms is rich of cases where changes have been attempted, without however to attain success. Likewise the Greek education system had experienced a lot of reforms, most of which have failed to make the intended changes and they attenuated shortly after their implementation or they ceased at the stage of legislative planning. On the other hand, the traditional research have failed to develop a coherent theoretical perspective and provide satisfactory interpretations of the perpetually unsuccessful reforms. This paper is part of wider project which attempts to address the above issue following the Complex Dynamical Systems (CDS) perspective, that is, by fostering the CDS epistemological assumptions and applying nonlinear methodological approaches. This endeavor focuses on teachers' readiness for change and explores the dimensions of the resistance to change related to the values, attitudes, dysfunction beliefs and planed behaviors of teachers. Given that the project is still ongoing, here, only the outline of the research design and the strategy followed are discussed along with some preliminary findings. At a first stage, the investigation implemented focus-group settings to reveal clues of those dimensions. The recorded data were analyzed via orbital decomposition analysis (ODA), a method designed for categorical time series and discourse analysis. Some of the crucial dimensions of resistance-to-change were subsequently measured via a survey instrument and were used to predict teachers' position with linear and nonlinear models. Statistical analysis showed that the cusp catastrophe model was superior to the linear alternatives and revealed discontinuities in teachers' positions, while certain variables proved to be bifurcation factors. The implications of these findings are discussed, while methodological aspects of ODA and catastrophe theory modeling are briefly presented. The present work sets a framework for the application of complexity theory and nonlinear dynamics in organizational theory of educational change.

This paper considers solving the real eigenvalues of the Quadratic Eigenvalue Problem (QEP) Q(\lambda)x =(\lambda^2M+\lambdaC+K)x = 0 in a given interval (a, b), where the coefficient matrices M, C, K are Hermitian and M is nonsingular. First, an inertia theorem for the QEP is proven, which characterizes the difference of inertia index between Hermitian matrices Q(a) and Q(b). Several useful corollaries are then obtained, where it is shown that the number of real eigenvalues of QEP Q(\lambda)x = 0 in the interval (a, b) is no less than the absolute value of the difference of the negative inertia index between Q(a) and Q(b); furthermore, when all real eigenvalues in (a, b) are semi-simple with the same sign characteristic, the inequality becomes an equality. Based on the established theory, the bisection method (with preprocessing) can be used to compute the real eigenvalues of the QEP by computing the inertia indices. Applications to the calculation of the equienergy lines with k.p ...

Validation of models that predict the performance of aerospace engine materials depends on the ability to obtain accurate single crystal elastic constants. Resonance Ultrasound Spectroscopy (RUS) is a nondestructive technique in which the natural resonances of a material are utilized to obtain these constants. Traditional RUS utilizes an analytic approach to determine the resonance frequencies of a specimen given an initial guess set of elastic constants. A nonlinear optimization process then fits the elastic constants to experimentally measured data. This approach is limited both in its ability to handle specimens with complex geometry and to handle polycrystalline materials. These more complex scenarios can be approached by utilizing a finite element forward model to obtain sample resonances.

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

In this paper we define three classes of new double sequence spaces. We give some relations related to these sequence spaces. We also introduce the concept of double lacunary statistical Zweier convergence and obtain some inclusion relations related to these new double sequence spaces.

This study used a logistic regression model to investigate the relationship between several predicting factors and burglary occurrence probability with regard to the epicenter. These factors include day of the week, time of the day, repeated victimization, connectors and barriers. Data was collected from a local police report on 2010 burglary incidents. Results showed the model has various degrees of significance in terms of predicting the occurrence within difference ranges from the epicenter. Follow-up refined multiple comparisons of different sizes were observed to further discover the pattern of prediction strength of these factors. Results are discussed and further research directions were given at the end of the paper.

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values. In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. Moreover, we work on the expansion problem based on the eigenfunctions of some linear operators. In addition, when the signals contain two different models, we develop a method that separate the signals in single-models and then solve the problem. We also consider the situation that when some of the sampling values are corrupted.

This work is designed to introduce electrochemists in a tutorial manner to the basics of modeling of electrochemical systems based primarily on diffusion equations. There is an introduction to analytical and numerical methods with examples taken from typical electrochemical experiments. The Laplace transform is used to derive the Cottrell equation and chronopotentiometry. The response of an electrode to a Gaussian concentration profile is detailed. Laplace's equation is solved for a simple cell to determine the potential distribution. Discrete methods are employed to calculate the current time behavior following a potential step using the explicit finite difference method. Cyclic voltammetry is simulated using the explicit, implicit and hopscotch methods along with the method of orthogonal collocation. In each case the steps used to solve the problem are comprehensively detailed.

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter e. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter e affects the geometry as well as the basin entropy of the convergence regions. The convergence areas are related with the required number of iterations and also with the corresponding probability distributions.

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ 1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝα with optimal state u ĝαα and optimal adjoint state p ĝαα are convergent as α → ∞ (in norm of a suitable Sobolev parabolic space) to ĝ, u ĝ and p ĝ , respectively, where the limit problem has Dirichlet (instead of Robin) boundary conditions on Γ 1 . The main techniques used are derived from the parabolic variational inequality theory.

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial ( ) . From a n n × Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix r L , supposed to provide a good estimation of the roots. By application of Gershgorin's theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy's bounds, Montel's bounds and Carmichel-Mason's bounds. According to the starting formel of r L , we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.

This paper follows NetSci High, a decade-long initiative to inspire teams of teenage researchers to develop, execute and disseminate original research in network science. The project introduced high school students to the computer-based analysis of networks, and instilled in the participants the habits of mind to deepen inquiry in connected systems and statistics, and to sustain interest in continuing to study and pursue careers in fields involving network analysis. Goals of NetSci High ranged from proximal learning outcomes (e.g., increasing high school student competencies in computing and improving student attitudes toward computing) to highly distal (e.g., preparing students for 21 century science), with an emphasis on doing real-world research into relevant and ambiguous problems through technologically-infused and highly collaborative projects and defending them to a clear (and sometimes potentially intimidating) audience. The cognitive goals of the project covered broad areas...

We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second-order twostep method with numerical solutions of differential equations (2orderND), and the second-order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear mixed model at the second step. We apply the proposed methods to the analysis of the Ditropan data, and evaluate their performance using a simulation study. Our results show that the 2orderND method performs well, while the 2orderAD method can yield PK parameter estimators that are subject to considerable biases.

In this paper, a numerical method is developed to approximate the soliton solutions of some nonlinear wave equations in terms of the Jacobi polynomials. Wave are very important phenomena in dispersion, dissipation, diffusion, reaction, and convection. Using the wave variable converts these nonlinear equations to the nonlinear ODE equations. Then, the operational Collocation method based on Jacobi polynomials as bases is applied to approximate the solution of ODE equation resulted. In addition, the intervals of the solution will be extended using an rational exponential approximation (REA). The KdV, Boussinesq, and Kaup–Kuperschmidt equations are studied as the test examples. Finally, numerical computation of the conservation values shows the effectiveness and stability of the proposed method.

We compute the numerical solution of Bratu's boundary value problem (BVP). To achieve this, we apply a new and useful approach to solve Bratu's boundary value problem by using Green's function and a new integral operator, along with a modified version of the Adomian decomposition method. This process produces solutions that call for the boundary conditions to be applied explicitly. Statistical results demonstrating the robustness and efficiency of the proposed scheme are included. An exact and approximate solution comparison is made with known results. The quantitative outcomes showcase our novel approach's high numerical precision and consistency across a range of parameter configurations. This is an open access article under the CC BY-SA license.

Reliable tsunami early warning forecasts rely on accurate initial modeling conditions and interpretations of subduction zone behavior in a multi-century perspective. GPS and seismologic data were introduced this past century to study rupture dynamics in detail, however limited information is known about ruptures that pre-date the 20 th century. I propose a methodology that uses statistics to better understand these pre-20 th century ruptures. This methodology applies the historical and geologic tsunami record as a means to select a suite of tsunami simulations from earthquake source solutions. I chose south-central Chile (46°S to 30°S) to test this new methodology; it has an extensive earthquake historical record at 47 different coastal sites, some of which date to the 16 th century. Between 1570 and 1960, this region experienced at least 17 tsunamigenic earthquakes. In addition to evaluating possible source solutions for these earthquakes, my methodology also allows the test of whether subducted fracture zones, like the Mocha fracture zone (MFZ) in south-central Chile, controls rupture propagation (as previously hypothesized). For this research, I used GeoClaw, a numerical tsunami modeling code, to simulate 423 forward-modeled M w iv 8.7-9.5 earthquake scenarios with stochastic, variable slip distributions. I used Akaike's Information Criterion (AIC) to identify significant earthquake parameters (M w and slip location) of 17 events by statistically selecting source models that had similar simulated wave heights to known observations in the historic and geologic record. For example, I concluded from AIC that the 1960 event was a M w 9.3 rupture with high slip concentration (~ 30 m) at ~ 39-40ºS, and the 1730 event was a M w 9.3 rupture with shallow maximum slip at ~ 36ºS; both solutions support the MFZ hypothesis. The AIC results generally agree with previously estimated magnitudes within the literature and were validated by using root mean square error RMSE values. I produced high resolution maps at three coastal sites with well-known tsunami observations for further refinement of potential rupture scenarios. Defining historical rupture characteristics gives insight regarding temporal and spatial variabilities of locking zones. This information may be useful for predicting future near-field tsunami wave heights for particularly vulnerable coastal regions. v ACKNOWLEDGMENTS Before I get into my more personal acknowledgments, I first want to acknowledge the Central Washington University School of Graduate Studies and Research for providing me with my graduate assistantships for the past two years. Also, I would like to acknowledge the National Science Foundation for providing funding to this research with grant EAR-1624542 awarded to Dr. Lisa Ely and Dr. Breanyn MacInnes. Now, I would like to give a big thank you to my advisor, Bre, for her guidance during the process of completing this project. I especially would like to acknowledge her patience and encouragement when it came to teaching me how to model tsunamisthis is a skill I am very grateful to have learned and one that I am very excited to apply towards my career. I could not have asked for a better advisor. I would also like to thank my "co-advisor," Walter, for teaching me how to fish, rather than just giving me a fish. I now have an understanding of how to code in Python, which will prove to be useful when I enter the workforce. Also, thanks for talking sports with me whenever I needed a break from this project. Additionally, my final committee member, Lisa, has been a tremendous help to me throughout this project-especially when it came to learning about the tsunami historical record of Chile. Traveling to Chile with you and the rest of the field team was a wonderful experience I will never forget. With that said, I'd also want to acknowledge Pachi for her absolutely extraordinary cooking during our field season. Those were an extra 10 pounds, I would be glad to get back. vi Also, thank you Craig Scrivner, Catherine Jeffries, and Ben Norford: Craig for your help setting me up on the Linux machines and walking me through many UNIX commands/error messages. Catherine for your Linux help and answering all my calls to help me troubleshoot GeoClaw when I would accidentally crash it. And Ben for helping me with making my fault model. Shout out to "the Fellas" at 14 th Ave and the "Earthquakers" for all good times, memories, and making my CWU experience worthwhile. Lastly, thank you to Alec Melone for lending me your snowshoes that I used to summit Mt. St. Helens. Here is your acknowledgment that I promised.

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In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate analytical solutions of the models, we design here a numerical technique to consistently approximate the system evolution dynamics, guaranteeing that nonnegative initial conditions will evolve uniquely into new, nonnegative approximations. This property of our technique is established using the theory of M-matrices, which are nonsingular matrices where all the entries of their inverses are posit...

The study focuses on the behavior of diffusion phenomenon in the normal and stenosed capillarytissue exchange system where the rheology of flowing blood in the capillary is characterized by the generalized Casson's fluid model. Assessment of the severity of the disease could be made possible through the variation of a parameter named as retention parameter. The concentration profile and associated physiological diffusion variable involved in the study for normal and diseased state have been analyzed. The model is also employed to study the effect of shape of stenosis on flow characteristics. An extensive quantitative analysis is performed through numerical computations of the desired quantities having physiological relevance through their graphical representations so as to validate the applicability of the present model.

In this work, we consider a single server unreliable retrial queue with sate dependent service and batch arrivals. Here the customers arrive according to a compound Poisson process that receives service immediately if the server is available or enter a retrial orbit. During the busy state the server faced breakdown and is then sent for repair. Before providing repair, the repairman takes some time to make its preliminary settings; this time is referred as delayed repair time. Here the customer leaves the system on service completion or rejoins the system for another service due to Bernoulli feedback. The unreliable server may leave for J-optional vacations whenever the queue is empty. We assume that the retrial times, service times and repair times are arbitrarily distributed. Using supplementary variable technique and probability generating function methods, we derive the system size distribution at random epoch and various other performance indices.

Modeling of inventory problems provides a good insight to retailers and distributors to maintain stock of different items such as seasonal products, perishable goods and daily useable goods etc. The deterioration of all these items exists to a certain extent due to several reasons like mishandling, evaporation, decay, environmental conditions, transportation etc. It is found from the literature that previously many of the researchers have developed inventory model ignoring deterioration and drawn conclusion. In the absence of deterioration parameter, an inventory model cannot be completely realistic. In this paper, we have made an attempt to extend an inventory model with ramp-type demand and price discount on back order where deterioration was not taken into account. In our study, deterioration and constant holding cost are taken into consideration keeping all other parameters same. As a result, the inventory cost function is newly constructed in the presence of deterioration. The ...

On December 31, 2019, a case of pneumonia with unknown cause was reported for the first time in Wuhan, China, to the World Health Organization (WHO). The outbreak was declared an international public health emergency on January 30, 2020, and on February 11 the viral respiratory disease caused by the new coronavirus was officially named COVID-19, or SARS-Cov-2. Figure 1 presents the data from the Secretary of Health of México on the dynamics and outcomes of the disease caused by SARS-Cov-2, showing that a mitigation strategy in the spread curve is necessary [1]. Mathematical models are useful to predict the temporal evolution of infectious diseases such as COVID-19 [2], one of the most used is the called susceptible-infected-recovered also known as SIR. With the purpose to estimate the real number of active infected, accumulated infected and recovered in the city of Tijuana, the proposed model and the information corresponding to the number of deaths registered on the Government's 'Monitoring of COVID-19 cases' page of Baja California that is updated daily with new statistics will be used [3].

A recent parameter identification technique, the local lagged adapted generalized method of moments, is used to identify the time-dependent disease transmission rate and time-dependent noise for the stochastic susceptible, exposed, infectious, temporarily immune, susceptible disease model (S E I RS) with vital rates. The stochasticity appears in the model due to fluctuations in the time-dependent transmission rate of the disease. All other parameter values are assumed to be fixed, known constants. The method is demonstrated with US influenza data from the 2004-2005 through 2016-2017 influenza seasons. The transmission rate and noise intensity stochastically work together to generate the yearly peaks in infections. The local lagged adapted generalized method of moments is tested for forecasting ability. Forecasts are made for the 2016-2017 influenza season and for infection data in year 2017. The forecast method qualitatively matches a single influenza season. Confidence intervals are given for possible future infectious levels. Keywords Compartment disease model • Stochastic disease model • Local lagged adapted generalized method of moments • Time-dependent transmission rate Mathematics Subject Classification 60H10 • 60P10 • 92D30