We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.

There exists a significant body of work on determining the acquisition number at(G) of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected acquisition number E(at(Pn)) of the n-path when n distinguishable "units" of integral weight, or chips, are randomly distributed across its vertices between 0.242n and 0.375n. With computer support, we improve it by showing that E(at(Pn)) lies between 0.29523n and 0.29576n. We then use subadditivity to show that the limiting ratio lim E(at(Pn))/n exists, and simulations reveal more exactly what the limiting value equals. The Hoeffding-Azuma inequality is used to prove that the acquisition number is tightly concentrated around its expected value. Additionally, in a different context, we offer a non-optimal acquisition protocol algorithm for the randomly weighted path and exactly compute the expected size of the resultant residual set.

Maxwell's equations for the electromagnetic field are symmetrized by introducing magnetic charges into the formalism of electrodynamics. The symmetrized equations are solved for the fields and potentials of point particles. Those potentials, some of which are found to be singular along a line, are used to formulate the Lagrangian for a system of two dyons (particles with both electric and magnetic charge). The equations of motion are derived from the Lagrangian. It is shown that the dimensionality constants k and k * , which we r e introduced to define the units of the electromagnetic fields, have to be equal in order to avoid center of mass acceleration in the two dyon system.

No description available.

We present a method for solving the Einstein-Maxwell equations in a five dimensional, asymptotically flat, black hole spacetime with three commuting Killing vector fields. In particular, we show that by reducing the dimension of the Einstein-Maxwell equations in a Kaluza-Klein like manner we can determine the components of the metric and vector potential which lie in the direction of the Killing vector fields. These components are determined by nine scalar fields each of which satisfy a partial differential equation in two variables. These equations take the form of an elliptic operator set equal to a nonlinear source. We find evidence that particular combinations of these fields satisfy Dirichlet boundary conditions, and are well suited to numerical solution using Green functions. Using this method we generate numerical solutions to the 4+1 Einstein-Maxwell equations corresponding to charged generalizations of the Myers-Perry solution. We also discover symmetry relations among the scalar equations which constrain their functional forms and posit the existence of two rigidity-theorem-like relations for electrovac spacetimes and sketch how their use generalizes our method to N+1 dimensions.

The Finite Element Tearing and Interconnecting (FETI) and its variants are probably the most celebrated domain decomposition algorithms for partial differential equation (PDE) scientific computations. In electromagnetics, such methods have advanced research frontiers by enabling the full-wave analysis and design of finite phased array antennas, metamaterials, and other multiscale structures. Recently, closer scrutiny of these methods have revealed robustness and numerical scalability problems that prevent the most memory and time efficient variants of FETI from gaining widespread acceptance. This work introduces a new class of FETI methods and preconditioners that lead to exponential iterative convergence for a wide class of problems, are robust and numerically scalable. First, a two Lagrange multiplier (LM) variant of FETI with impedance transmission conditions, the FETI-2λ, is introduced to facilitate the symmetric treatment of non-conforming grids while avoiding matrix singularites that occur at the interior resonance frequencies of the domains. A thorough investigation on the approximability and stability of the Lagrange multiplier discrete space is carried over to identify the correct LM space basis. The resulting method, although accurate and flexible, exhibits unreliable iterative convergence. To accelerate the iterative convergence, the Locally Exact Algebraic Preconditioner (LEAP), which is responsible for improving the information transfer between neighboring domains is introduced. The LEAP was conceived by carefully studying the properties of the Dirichlet-to-Neumann (DtN) map that is involved in the sub-structuring process of FETI. LEAP proceeds in a hierarchical way and directly factorizes the signular and near-singular interactions of the DtN map that arise from domain-face, domain-edge and domain-vertex interactions. For problems with small number of domains LEAP results in scalable implementations with respect to the discretization. On problems with large domain numbers, the numerical scalability can only be obtained through ``global'' preconditioners that directly convey information to remotely separated domains at every DDM iteration. The proposed ``global" preconditiong stage is based on the new Multigrid FETI (MG-FETI) method. This method provides a coarse grid correction mechanism defined in the dual space. Macro-basis functions, that satisfy thecurl-curl equation on each interface are constructed to reduce the size of the coarse problem, while maintaining a good approximation of the characteristic field modes. Numerical results showcase the performance of the proposed method on one-way, 2D and 3D decomposed problems, with structured and unstructured partitioning, conforming and non-conforming interface triangulations. Finally, challenging, real life computational examples showcase the true potential of the method.

Flexographic printing involves driving a paper substrate through the gap between two cylinders, where one of the cylinders has a print form layer covered in ink. The ink transfer from the print form to the paper is dependent on the pressure between the paper substrate and the cylinders. Knowledge about how the paper substrate reacts to compression is therefore important when aiming for high quality flexography printing. In this project the paper substrate in focus is corrugated board consisting of a top liner, a bottom liner and a fluted paper material in between the liners. To gain knowledge about the compression dynamics of the boards they are subjected to compression experiments with and without print form. The compression experiments are filmed and the videos are then analyzed using thresholding and tracking methods. The developed thresholding method is able to measure the thickness of each material separately in each frame while the developed tracking method is able to track the movement of the top and bottom metal blocks compressing the materials. The strains calculated from the image analysis measurements are then used as input values to the Maxwell spring-dashpot model with the intention of modelling the stress. Analysis of the compression experiment videos shows that the material properties of thecorrugated board may not be constant for the duration of the compression. This is because the fluting changes its shape when being compressed. Comparing the modelled stress to the stress measured by the press used in the experiments shows that the Maxwell spring-dashpot model is not able to model the stress accurately when the corrugated board goes through multiple stages of compression. The model works better for compression where the shape of the fluting is not significantly changed.

DNA (Deoxyribonucleic Acid) must be extracted from the cell before it can be amplified using the PCR (Polymerase Chain Reaction) to generate an STR (Short Tandem Repeat) profile. Although extraction methods such as binding DNA to silica remove PCR inhibitors, they have complex procedures that can lead to partial DNA loss. Evaluating the efficiency of an extraction method can be difficult, as the original amount of input DNA may be unknown. Knowledge of the amount of DNA expected to be present in a sample can provide quantitative information on an extraction method’s efficiency, as the recovery of DNA from a DNA extraction process can be calculated using the expected DNA value. Theoretically, while using a direct lysis extraction method, all the cells in the sample are lysed and present in that single tube, so quantitative PCR (qPCR) values of samples extracted using a direct lysis method such as forensicGEMTM can be used as an expected yield value. Validation studies determine if a method is reliable, reproducible, and robust. An internal validation study, following the Federal Bureau of Investigation’s Quality Assurance Standards (QAS) for Forensic DNA Analysis Methods, was performed for the Maxwell® FSC instrument, a robotic DNA extraction instrument designed to remove PCR inhibitors from forensic samples. Results from this study were compared to results obtained on a previously validated Maxwell® 16 instrument. The validation study was successful, as the study demonstrated the instrument could process known/non-probative evidentiary samples, is sensitive, precise, accurate, can process mixture samples, and had no detectable contamination in the process. An added study, done post validation, compared the amount of DNA obtained using a “direct lysis method” with the amount of DNA obtained using samples equivalent to those used in the instrument validation. However, upon comparing the amount of DNA recovered using the Maxwell® FSC instrument to the amount of DNA obtained using a direct lysis method, which in theory would recover 100% of the DNA, the percent yield for serially diluted blood samples was low. Only 10.79% of the DNA was recovered for the 1:10 dilution, 14.44% was recovered for the 1:100 dilution, and 8.00% was recovered for the 1:1000 dilution. The DNA IQTM System – Small Sample Casework kit uses the same chemistry and the same reagents as the Maxwell® FSC DNA IQTM Casework Kit. To provide additional data on DNA recovery, the Maxwell® FSC Study was replicated using the DNA IQTM System – Small Sample Casework Kit, following the manufacturer’s instructions for manual extractions. The study showed that about 77.71% of the DNA is lost when using neat samples, 96.88% is lost for the 1:10 dilution samples, 95.22% is lost for 1:100, and 99.00% for 1:1000. Steps from the DNA IQTM System – Small Sample Casework Protocol were identified where, potentially, the DNA loss could have occurred. These included DNA left in the waste products, DNA left on the swatch, and DNA left on the Resin after elution. Study data identify experimentally two major sources of DNA loss: the waste and the swatch. When quantifying the “waste,” for almost every individual sample, more DNA remained in the waste than was found in the initial extract using the DNA IQTM System – Small Sample Casework Kit. The high amounts of DNA in the waste indicates that the DNA IQ™ Resin does not bind to all the available nucleic acid in the solution. The data and other data characterizing DNA loss at particular steps of the protocol are described in this study. Modifications to the protocol are described, which were made, in an attempt, to increase the amount of DNA bound to the Resin that could subsequently be recovered. Laboratories that use DNA IQTM reagents need to be aware that a significant amount of the sample may be lost when following the procedure. Preliminary results indicate that yield can be improved by modifying the procedure to either increase the Resin volume, increase the incubation temperature, or recapture DNA from the first waste.

No description available.

<p>A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal derivation of the NLS approximation from the wave-Maxwell equation, we establish well-posedness and perform rigorous justification analysis to show smallness of error terms for appropriately small time intervals. We conclude by numerical simulation to illustrate the results in one-dimensional case.</p> / Master of Science (MSc)