No description available.

A physics-based model incorporating the UTC (uni-traveling carrier) photodiode (PD) in the limit of weak nonlinearity was used in order to characterize the effects of nonlinearity on high speed and high power photodiodes. The combined influences of a) optical illumination, b) photocurrent, and c) interaction of the photodiode with an external circuit, were incorporated into three equations which described the phasor dynamics of the photodiode, which could be used to approximate the diode voltage, the depletion region thickness, and the electric field at the beginning of the depletion region by the Newton-Raphson Method. Then a frequency response plot as well as a third-order intermodulation distortion (IMD3) plot were obtained in order to evaluate the effects of nonlinearity on the photodiode. The third-order intercept point (IP3) was determined to be approximately 27.5 dB, illustrating its slight nonlinearity. For both the frequency and the IMD3 plots, it was shown that modulation bandwidth is predominantly RC-limited and that the stated assumptions were true: that the average electron transit time through the depletion region is expected to be significantly smaller than the period of the optical stimulus. Finally, nonlinearity was minimized by compensating the heavy loading and space charge effects on junction capacitance, and a surface plot was obtained demonstrating this behavior.

A general framework for performance optimization of continuous-time OTA-C (Operational Transconductance Amplifier-Capacitor) filters is proposed. Efficient procedures for evaluating nonlinear distortion and noise valid for any filter of arbitrary order are developed based on the matrix description of a general OTA-C filter model . Since these procedures use OTA macromodels, they can be used to obtain the results significantly faster than transistor-level simulation. In the case of transient analysis, the speed-up may be as much as three orders of magnitude without almost no loss of accuracy. This makes it possible to carry out direct numerical optimization of OTA-C filters with respect to important characteristics such as noise performance, THD, IM3, DR or SNR. On the other hand, the general OTA-C filter model allows us to apply matrix transforms that manipulate (rescale) filter element values and/or change topology without changing its transfer function. The above features are a basis to build automated optimization procedures for OTA-C filters. In particular, a systematic optimization procedure using equivalence transformations is proposed. The research also proposes suitable software implementations of the optimization process. The first part of the research proposes a general performance optimization procedure and to verify the process two application type examples are mentioned. An application example of the proposed approach to optimal block sequencing and gain distribution of 8th order cascade Butterworth filter (for two variants of OTA topologies) is given. Secondly the modeling tool is used to select the best suitable topology for a 5th order Bessel Low Pass Filter. Theoretical results are verified by comparing to transistor-level simulation withCADENCE. For the purpose of verification, the filters have also been fabricated in standard 0.5mm CMOS process. The second part of the research proposes a new linearization technique to improve the linearity of an OTA using an Active Error Feedforward technique. Most present day applications require very high linear circuits combined with low noise and low power consumption. An OTA based biquad filter has also been fabricated in 0.35mm CMOS process. The measurement results for the filter and the stand alone OTA have been discussed. The research focuses on these issues.

This thesis applies continuous time Markov chain theory to develop three different models for financial applications.

Diss. Stockholm : Handelshögsk., 2003.

Diss. Stockholm : Handelshögskolan, 2006.

No description available.

Recent advances in biology have revolutionized our understanding of living systems. For the first time, it is possible to study the behavior of individual cells. This has led to the discovery of many amazing phenomena. For example, cells have developed intelligent mechanisms for foraging, communicating, and responding to environmental changes. These diverse functions in cells are controlled through biochemical networks consisting of many different proteins and signaling molecules. These molecules interact and affect gene expression, which in turn affects protein production. This results in a complex mesh of feedback and feedforward interactions. These complex networks are generally highly nonlinear and stochastic, making them difficult to study quantitatively. Recent studies have shown that biochemical networks are also highly modular, meaning that different parts of the network do not interact strongly with each other. These modules tend to be conserved across species and serve specific biological functions. However, detect- ing modules and identifying their function tends to be a very difficult task. To overcome some of these complexities, I present an alternative modeling approach that builds quantitative models using coarse-grained biological processes. These coarse-grained models are often stochastic (probabilistic) and highly non-linear. In this thesis, I focus on modeling biochemical networks in two distinct biological systems: Dictyostelium discoideum and microRNAs. Chapters 2 and 3 focus on cellular communication in the social amoebae Dictyostelium discoideum. Using universality, I propose a stochastic nonlinear model that describes the behavior of individual cells and cellular populations. In chapter 4 I study the interaction between messenger RNAs and noncoding RNAs, using Langevin equations.

No description available.

This work explores the physics of micro and nano-scale systems immersed in a fluid. Previous literature has established an understanding of the fluid-solid interaction for systems including cantilevers and doubly clamped beams. Building on these advances, this work extends the theory of doubly clamped beams with an arbitrary amount of tension. Both the driven and stochastic dynamics of a doubly clamped beam are explored. The driven dynamics are investigated for a spatially applied harmonic driving force, and demonstrates quantitative agreement with an experimental beam that is driven electrothermally, in both air and in water. For the stochastic dynamics, the noise spectrum describes the thermal fluctuations at a given frequency. The theoretical model provides an analytical expression for the noise spectrum from an arbitrary number of modes. The noise spectrum of the first eleven modes are computed, and show excellent agreement with the noise spectrum from finite element simulations, which is computed from the deterministic ring down. This agreement is shown across different fluids (air and water), and for multiple measuring points including at the beam midpoint and the quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force by modifying the Young's modulus. This work defines the Young's modulus such that the restoring force is like a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. To understand the stochastic dynamics of the virtual beam, the stochastic Duffing oscillator is solved numerically. The ensemble autocorrelation of the beam dynamics are investigated for nonlinearities varying from linear to strongly nonlinear. The numeric autocorrelation is used to quantify the range of nonlinear strength where a deterministic approach, the ring down, can yield a good approximation. In the strongly nonlinear regime, the stochastic numerical approach is used to determine the autocorrelation. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center. / Doctor of Philosophy / This work explores the physics of small systems immersed in a fluid, such as air or water. Previous literature has established an understanding of the force from a fluid acting on solids such as cantilevers and doubly clamped beams. Building on these advances, this work extends theory to doubly clamped beams with any amount of tension. Both the driven and stochastic, or randomly driven, dynamics of a doubly clamped beam are explored. The driven dynamics are developed for a driving force applied over part of the beam, and demonstrates quantitative agreement with an experimental beam, in both air and in water. For the stochastic dynamics, the noise spectrum describes the random thermal fluctuations of the beam at a given frequency. These thermal fluctuations are small, but measureable deviations of the system from equilibrium and are significant for these small scale systems. The noise spectrum can be estimated by computing the statistics from many randomly forced simulations. However, previous literature provides a direct computation of the noise spectrum with a single deterministic ring down. This work provides an analytical expression for the noise spectrum of a doubly clamped beam in tension in fluid for multiple modes. The theoretical noise spectrum shows excellent quantitative agreement with the ring down from finite element simulations. The agreement between theory and simulation is demonstrated in air and water, for a measurement of the noise spectrum at the beam midpoint and at the beam quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force such that the system becomes increasingly stiff as the displacements become larger. This definition results in the restoring force following a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. For varying nonlinear strengths, the stochastic numerical approach is used to quantify the dynamics, and the range of usefulness for the deterministic ring down is investigated. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center.