Markov Chain Theory with Applications to Baseball

The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing baseball as a Markov chain. The final chapter describes this Markov chain model for baseball, which we will use to calculate the expected number of runs scored for the 2013 College of Wooster baseball team. This paper finishes by displaying an analysis of sacrifice bunt and stolen base strategies through using the Markov chain model

Magnetoplasmonic Interferometers and Applications

Comunicación presentada en el 2nd Early Stage Researchers Workshop in Nanoscience, celebrado en Madrid el 28 y 29 de junio de 2012.Surface plasmons polaritons (SPP) are evanescent waves that propagate along a dielectric-metal interface. They can be confined in subwavelength metal structures, i.e. below the diffraction limit, which leads to many possible applications, including miniaturized optical devices. Within that context, the development of active plasmonics is important to achieve nanophotonic devices with advanced functionalities. This requires a system where the plasmon properties can be manipulated using an external agent. Among the different control agents considered so far, the magnetic field seems a promising candidate, since it is able to modify the dispersion relation of SPP at reasonable magnetic field strengths, and with a high switching speed. This modulation comes from the non-diagonal elements of the dielectric tensor, εij, appearing when the magnetic field is turned on. For noble metals, the ones typically used in plasmonics, these elements are proportional to the applied magnetic field but, unfortunately, very small at field values reasonable for developing applications. On the other hand, ferromagnetic metals have sizeable εij values at small magnetic fields (proportional to their magnetization), but are optically too absorbent. A smart system to develop magnetic field tunable plasmonic devices is the use of multilayers of noble and ferromagnetic metals. That is the framework of the present work, where we analyze the magnetic field induced SPP wavevector modulation (Ak) in Au/Co/Au films as a function of the wavelength and its possible application as a sensor.N

Testing a discrete model for quantum spin with two sequential Stern-Gerlach detectors and photon Fock states

Despite its unparalleled success, quantum mechanics (QM) is an incomplete theory of nature. Longstanding concerns regarding its mathematical foundations and physical interpretation persist, a full century beyond its conception. Limited by these issues, efforts to move beyond QM have struggled to gain traction within the broader physics community. One approach to progress in this direction, which is deeply rooted in the tradition of physics, is the development of new models for physical systems otherwise treated by QM. One such model is presented here, which concerns the interaction of a spin system with sequences of two Stern-Gerlach detectors that may be independently rotated. Rather than employing the traditional formalism of QM, the proposed model is supported by tools from discrete mathematics, such as finite groups, set theory, and combinatorics. Equipped with this novel toolkit, an analog of Wigner's d-matrix formula is derived and shown to deviate slightly from QM. With these results, the proposed model is extended to an optical system involving photon number states passing through a beam splitter. Leveraging recent advancements in high precision experiments on these systems, we then propose a means of testing the new model using a tabletop experiment. Hence, the proposed model not only makes clear testable predictions, but also provides valuable insight into the essential principles of quantum theory.Comment: 20 pages, 6 figure

Imaging and Discrimination of High-Z Materials with Muon Scattering Tomography

Technical paper presented at the 2017 Defence and Security Doctoral Symposium.We have developed methods to define the edges of uranium blocks embedded in concrete, and to discriminate them from different high-Z materials, using muon scattering tomography. There is a need to characterise containers of nuclear waste without having to open them. This is particularly important for legacy waste, which includes large containers with unknown materials. Muon scattering tomography uses as probes the natural occurring cosmic muons, which are highly penetrating particles. Muons undergo multiple Coulomb scattering in matter, and the amount of scattering depends on the atomic number Z of the material, so it is possible to perform imaging of different materials by measuring the incoming and outgoing muon tracks. We carried out simulations in Geant4 of uranium objects of different lengths, enclosed in concrete. These lengths were measured with a new algorithm and compared to the simulated lengths, resulting in a resolution of 0.9 mm, with a 0.2 mm error. The smallest length measured was a uranium sheet with a width of 2 mm. In the material discrimination study, a multivariate analysis was performed with the variables obtained, such as scatter angle distribution, and other correlated variables, in order to distinguish materials from different simulations with the same geometry. Cubic blocks of different sizes and materials were simulated, with sides ranging from 2 cm to 10 cm, with scanning times ranging from a few hours up to 80 hours depending on the sizes of the blocks. From these simulations, we show that it is possible to distinguish uranium blocks from lead, tungsten and plutonium blocks of the same size. The smallest blocks with a good discrimination were cubes with 2 cm side.AW

Self-assembled MgxZn1−xO quantum dots (0 ≤ x ≤ 1) on different substrates using spray pyrolysis methodology

By using the spray pyrolysis methodology in its classical configuration we have grown self-assembled MgxZn1−xO quantum dots (size [similar]4–6 nm) in the overall range of compositions 0 ≤ x ≤ 1 on c-sapphire, Si (100) and quartz substrates. Composition of the quantum dots was determined by means of transmission electron microscopy-energy dispersive X-ray analysis (TEM-EDAX) and X-ray photoelectron spectroscopy. Selected area electron diffraction reveals the growth of single phase hexagonal MgxZn1−xO quantum dots with composition 0 ≤ x ≤ 0.32 by using a nominal concentration of Mg in the range 0 to 45%. Onset of Mg concentration about 50% (nominal) forces the hexagonal lattice to undergo a phase transition from hexagonal to a cubic structure which resulted in the growth of hexagonal and cubic phases of MgxZn1−xO in the intermediate range of Mg concentrations 50 to 85% (0.39 ≤ x ≤ 0.77), whereas higher nominal concentration of Mg ≥ 90% (0.81 ≤ x ≤ 1) leads to the growth of single phase cubic MgxZn1−xO quantum dots. High resolution transmission electron microscopy and fast Fourier transform confirm the results and show clearly distinguishable hexagonal and cubic crystal structures of the respective quantum dots. A difference of 0.24 eV was detected between the core levels (Zn 2p and Mg 1s) measured in quantum dots with hexagonal and cubic structures by X-ray photoemission. The shift of these core levels can be explained in the frame of the different coordination of cations in the hexagonal and cubic configurations. Finally, the optical absorption measurements performed on single phase hexagonal MgxZn1−xO QDs exhibited a clear shift in optical energy gap on increasing the Mg concentration from 0 to 40%, which is explained as an effect of substitution of Zn2+ by Mg2+ in the ZnO lattice