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This paper studies the relationship between the degree of compactness of the pile structure foundation and how it will tilt under different wave condition. In the lab experiment setup, we use a periodic force generated by a magnetic coil to simulate the wave force impending on a scaled down model pile. With this setup, forces with different periods and magnitudes are used to find out the critical wave condition under which the pile will tilt, and it relationship with the results, engineering aspect of setting up a pile structure in the sea will have a better reference in the design stage.

Hyperkalemic periodic paralysis (HyperKPP) is an autosomal dominant human skeletal muscle channelopathy that causes periods of myotonic discharge and periodic paralysis due to defective Nav1.4 sodium channels. Patients are asymptomatic at birth, attacks become short and frequent during childhood, and more severe during adolescence. Since the Nav1.4 content in the cell membrane is relatively constant during childhood, it was hypothesized that some symptoms start with the defective Nav1.4 channels, while other symptoms start after some changes occur in gene expression affecting other membrane channel content and/or activity. To test the hypothesis, the contractile characteristics of EDL and soleus muscles from HyperKPP mice from the age of 0.5 to 12 months were tested in vitro. For both EDL and soleus, contractile defects, including low force generation, instability and large unstimulated force were observed by two weeks of age. With aging, the defects did not worsen, but muscles actually showed some improvement. Considering that Nav1.4 protein content reaches maximum at three weeks of age, the data suggests that HyperKPP symptoms are solely due to the defective Nav1.4 channels.

Hyperkalemic periodic paralysis (HyperKPP) is an autosomal dominant human skeletal muscle channelopathy that causes periods of myotonic discharge and periodic paralysis due to defective Nav1.4 sodium channels. Patients are asymptomatic at birth, attacks become short and frequent during childhood, and more severe during adolescence. Since the Nav1.4 content in the cell membrane is relatively constant during childhood, it was hypothesized that some symptoms start with the defective Nav1.4 channels, while other symptoms start after some changes occur in gene expression affecting other membrane channel content and/or activity. To test the hypothesis, the contractile characteristics of EDL and soleus muscles from HyperKPP mice from the age of 0.5 to 12 months were tested in vitro. For both EDL and soleus, contractile defects, including low force generation, instability and large unstimulated force were observed by two weeks of age. With aging, the defects did not worsen, but muscles actually showed some improvement. Considering that Nav1.4 protein content reaches maximum at three weeks of age, the data suggests that HyperKPP symptoms are solely due to the defective Nav1.4 channels.

We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. It involves smoothing the singular Green's functions in the integrands and finding correction terms to the resulting smooth integrals. The analytical method is based on the singular integral methods of J. Thomas Beale, while the scattering problem is motivated by the 2D work of Stephanos Venakides, Mansoor Haider, and Stephen Shipman. The 3D problem was done with boundary element methods by Andrew Barnes. We present a method that is both more straightforward and more accurate. In solving these problems, we have used the M\"{u}ller integral equation formulation of Maxwell's equations, since it is a Fredholm integral equation of the second kind and is well-posed. M\"{u}ller derived his equations for the case of a compact scatterer. We outline the derivation and adapt it to a periodic scatterer. The periodic Green's functions found in the integral equation contain singularities which make it difficult to evaluate them numerically with accuracy. These functions are also very time consuming to evaluate numerically. We use Ewald splitting to represent these functions in a way that can be computed rapidly.We present a method of smoothing the singularity of the Green's function while maintaining its periodicity. We do local analysis of the singularity in order to identify and eliminate the largest sources of error introduced by this smoothing. We prove that with our derived correction terms, we can replace the singular integrals with smooth integrals and only introduce a error that is third order in the grid spacing size. The derivation of the correction terms involves transforming to principal directions using concepts from differential geometry. The correction terms are necessarily invariant under this transformation and depend on geometric properties of the scatterer such as the mean curvature and the differential of the Gauss map. Able to evaluate the integrals to a higher order, we implement a \mbox{GMRES} algorithm to approximate solutions of the integral equation. From these solutions, M\"{u}ller's equations allow us to compute the scattered fields and transmission coefficients. We have also developed acceleration techniques that allow for more efficient computation.We provide results for various scatterers, including a test case for which exact solutions are known. The implemented method does indeed converge with third order accuracy. We present results for which the method successfully resolves Wood's anomaly resonances in transmission. / Dissertation

<p>This thesis reviews the experimental investigation of a non-smooth dynamical system consisting of two pendula; a large pendulum attached to a frame with an impact wall, and a small pendulum, which shares its axis of rotation with the large pendulum and can impact against the large pendulum. The system is forced with a sinusoidal horizontal motion, and due to the nonlinearities present in pendula as well as the discontinuous forcing from impacts, exhibits a wide range of behavior. Periodic, quasi-periodic, and chaotic responses all are possible, hysteresis is present, and grazing bifurcations allow for spontaneous change of behavior and the appearance of chaotic responses without following a traditional route to chaos. This thesis follows from existing non-linear dynamics research on forced pendula, impacting systems (such as a bouncing ball) and doubly impacting systems (ball bouncing on top of a bouncing ball).</p> / Thesis

Many researchers had developed polyphase sequences, so called ¡§perfect sequence¡¨ or ¡§ideal sequence¡¨, with ideal periodic auto-correlation function. There are lots of applications of communication system depends on the sequences with good auto-correlation property, i.e., synchronization, channel estimation and multiple access. These sequences cannot maintain the ideal property in implementation, because of the error of quantization in digital signal processing of transmitter. On the contrary, we develop a novel set of perfect sequences, Gaussian Integer Perfect Sequence (GIPS), which only contains Gaussian integers. In this paper, we construct them by linear combination and cyclic shift of the eight base sequences. We present the design and basic properties of the sequences. Furthermore, the design method of sequences with the smallest dynamic range is presented.

We investigate the number of periodic points of certain discrete quadratic maps modulo prime numbers. We do so by first exploring previously known results for two particular quadratic maps, after which we explain why the methods used in these two cases are hard to adapt to a more general case. We then perform experiments and find striking patterns in the behaviour of these general cases which suggest that, apart from the two special cases, the number of periodic points of all quadratic maps of this type behave the same. Finally we formulate a conjecture to this effect.

In this thesis we study the number of periodic points of congruential monomial dynamical system. By concept of index calculus we are able to calculate the number of solutions for congruential equations. We give formula for the number of r-periodic points over prime power. Then we discuss about calculating the total number of periodic points and cycles of length r for prime power.