We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In the literature, most studies of ultraviolet cutoffs are concerned with Lorentz-violating ultraviolet cutoffs. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. It was shown that this problem is avoided by the proposed covariant cutoff by allowing field modes with arbitrarily small wavelengths to still exist, albeit with exceedingly small, covariantly-determined bandwidths. In other words, the degrees of freedom of sub-Planckian modes in time are highly suppressed. The effects of this covariant ultraviolet cutoff on the kinematics of a scalar quantum field are well understood. There is much to learn, however, about the effects on a field’s dynamics. These effects are of great interest, as their presence may have direct observational consequences in cosmology. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics at the Planck scale. In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics of the CMB encodes information about the quantum fluctuations of the scalar inflaton field. A measure of the strength of a field’s quantum fluctuations is in turn given by the magnitude of the field’s Feynman propagator. To this end, in this thesis I study how this covariant ultraviolet cutoff modifies the Feynman propagator of a scalar quantum field. In this work, I first calculate the cutoff Feynman propagator for a scalar field in flat spacetime, and then I address the cutoff Feynman propagator of a scalar field in curved spacetime. My studies culminate with an explicit calculation for the case of a power-law Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. This last calculation is cosmologically significant, as power-law FLRW spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary back- ground material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.

The characteristics of slotted circular waveguides with different dimensions, including cutoff frequencies of TE and TM modes, impedance and modal field distributions will be analyzed using the generalized spectral domain approach. The Method of Moment will be applied, basis functions that include the edge conditions will be used and a computer program will be developed. Obtained results will be presented for different number, depth and thickness of coupling slots, and compared with available data to demonstrate the accuracy and the efficiency of the approach. Plots of the electric and magnetic field lines corresponding to the dominant as well as a number of higher order modes will be presented for quadruple ridge case.

In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In the literature, most studies of ultraviolet cutoffs are concerned with Lorentz-violating ultraviolet cutoffs. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. It was shown that this problem is avoided by the proposed covariant cutoff by allowing field modes with arbitrarily small wavelengths to still exist, albeit with exceedingly small, covariantly-determined bandwidths. In other words, the degrees of freedom of sub-Planckian modes in time are highly suppressed. The effects of this covariant ultraviolet cutoff on the kinematics of a scalar quantum field are well understood. There is much to learn, however, about the effects on a field’s dynamics. These effects are of great interest, as their presence may have direct observational consequences in cosmology. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics at the Planck scale. In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics of the CMB encodes information about the quantum fluctuations of the scalar inflaton field. A measure of the strength of a field’s quantum fluctuations is in turn given by the magnitude of the field’s Feynman propagator. To this end, in this thesis I study how this covariant ultraviolet cutoff modifies the Feynman propagator of a scalar quantum field. In this work, I first calculate the cutoff Feynman propagator for a scalar field in flat spacetime, and then I address the cutoff Feynman propagator of a scalar field in curved spacetime. My studies culminate with an explicit calculation for the case of a power-law Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. This last calculation is cosmologically significant, as power-law FLRW spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary back- ground material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.

A survey of relevant literature on the topic of wave propagation and scattering in pipes is given first. This review is followed by a theoretical framework which is pertinent to wave propagation in homogeneous, isotropic, pipes. Emphasis is placed on approximate solutions stemming from a computer based, Semi-Analytical Finite Element (SAFE) formulation. A modal analysis of the dynamic response of homogeneous, isotropic pipes, when subjected to a transient ultrasonic excitation, demonstrates that dominant features, i.e., singularities in an unblemished pipe’s displacement Frequency Response Function (FRF) coincide with its cutoff frequencies. This behaviour is confirmed experimentally. A novel technique is developed to deduce such a pipe’s wall thickness and elastic properties from three cutoff frequencies. The resulting procedure is simulated numerically and verified experimentally. Agreement between the new ultrasonic procedure and traditional destructive tests is within experimental uncertainty. Then a hybrid-SAFE technique is used to simulate waves scattered by various open rectangular notches. The simulations show, for the first time, that singularities distinct from the unblemished pipe’s cutoff frequencies arise in a displacement FRF when an axisymmetric notch is introduced. They also suggest that the new singularities depend on the properties of the parent pipe and the finite element region but effects are local to a notch. It is demonstrated further that the difference between the frequency at which a singularity introduced by a notch occurs and the nearest corresponding unblemished pipe’s cutoff frequency is a function of the notch’s dimensions. By plotting contours of constant frequency differences, it is shown that it is usually possible to characterize the notch’s dimensions by using two modes. However, the frequency difference for a third mode may be also needed occasionally. The more general case of nonaxisymmetric notches is shown to be a straightforward extension of the axisymmetric case.

A survey of relevant literature on the topic of wave propagation and scattering in pipes is given first. This review is followed by a theoretical framework which is pertinent to wave propagation in homogeneous, isotropic, pipes. Emphasis is placed on approximate solutions stemming from a computer based, Semi-Analytical Finite Element (SAFE) formulation. A modal analysis of the dynamic response of homogeneous, isotropic pipes, when subjected to a transient ultrasonic excitation, demonstrates that dominant features, i.e., singularities in an unblemished pipe’s displacement Frequency Response Function (FRF) coincide with its cutoff frequencies. This behaviour is confirmed experimentally. A novel technique is developed to deduce such a pipe’s wall thickness and elastic properties from three cutoff frequencies. The resulting procedure is simulated numerically and verified experimentally. Agreement between the new ultrasonic procedure and traditional destructive tests is within experimental uncertainty. Then a hybrid-SAFE technique is used to simulate waves scattered by various open rectangular notches. The simulations show, for the first time, that singularities distinct from the unblemished pipe’s cutoff frequencies arise in a displacement FRF when an axisymmetric notch is introduced. They also suggest that the new singularities depend on the properties of the parent pipe and the finite element region but effects are local to a notch. It is demonstrated further that the difference between the frequency at which a singularity introduced by a notch occurs and the nearest corresponding unblemished pipe’s cutoff frequency is a function of the notch’s dimensions. By plotting contours of constant frequency differences, it is shown that it is usually possible to characterize the notch’s dimensions by using two modes. However, the frequency difference for a third mode may be also needed occasionally. The more general case of nonaxisymmetric notches is shown to be a straightforward extension of the axisymmetric case.

The age-cutoff regression discontinuity design (RDD) has emerged as one of the most rigorous quasi-experimental approaches to determining program effects of prekindergarten on literacy and numeracy outcomes for children at kindergarten entry. However, few pre-K meta-analyses have focused attention on validity threats. The current random-effects meta-regression tests the moderating effects of prominent threats to validity, selection bias and sensitivity, on impact estimates generated from age-cutoff regression discontinuity studies from large-scale programs. Results from averaging dependent standardized mean difference effects suggested small positive moderating effects of total attrition and robust 3-month bandwidths on reading effects, but not on math. However, these results were not statistically significant. In contrast, results generated from robust variance estimation yielded a small statistically significant association between total attrition and math effects. These mixed results may warrant further research on prekindergarten evaluation methodology, evaluation estimation methods, and the totality of evidence used to inform policy.

This report explores if Monte-Carlo Tree Search (MCTS) can perform well in Fox Game, a classic Scandinavian strategy game. MCTS is implemented using a cutoff in the simulation phase. The game state is then evaluated using a heuristic function that is formulated using theoretical arguments from its chess counterpart. MCTS is shown to perform on the same level as highly experienced human players using limited computational resources. The method is used to explore how the imbalance in Fox Game (favoring sheep) can be mended by reducing the number of sheep pieces from 20 to 18. / I denna rapport undersöks om Monte-Carlo trädsökning (MCTS) kan prestera väl i rävspel, ett klassiskt skandinaviskt strategispel. MCTS implementeras med en cutoff i simuleringsfasen. Speltillståndet utvärderas där med hjälp av en heuristisk funktion som formuleras med hjälp av teoretiska argument från dess motsvarighet i schack. MCTS med endast begränsade beräkningsresurser visas kunna prestera på samma nivå som mycket erfarna människor. Metoden används för att utforska hur obalansen i rävspel (som gynnar får) kan förbättras genom att minska antalet fårpjäser från 20 till 18. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

La combustion pré mélangée a été depuis longtemps un domaine vaste d’étude au niveau appliqué et fondamental. Bien que la plupart des applications industrielles en combustion aient lieu dans des régimes turbulents, le passage par l’étude laminaire est indispensable pour comprendre les mécanismes fondamentaux des flammes turbulentes. Ce travail de thèse porte essentiellement sur l’étude des différentes instabilités agissant sur un front de flamme laminaire de pré mélange pour des mélanges de propane-air et méthane-air, enrichis ou non en azote. L’étude consiste à mesurer les taux de croissance des perturbations dans un brûleur d’Hele-Shaw formé par deux plaques de verre ($150\times50cm$) très rapprochées (brûleur 2D). Grâce à un système de forçage constitué par des plaques modulées spatialement avec différentes longueurs d’onde, le taux de croissance peut être mesuré même en présence du développement spontané de l’instabilité avec la longueur d’onde la plus instable. A richesse constante et pour des valeurs croissantes de la dilution en oxygène le vecteur d'onde de coupure augmente avec la vitesse de flamme qui devient plus instable. Pour des mélanges de propane ce nombre d’onde augmente également lorsqu'on augmente la richesse à vitesse constante et il diminue dans le cas des mélanges de méthane, cela est en relation avec l'évolution des effets thermodiffusifs dans chacun des cas. Une augmentation de l’épaisseur de la cellule d’Hele-Shaw, aboutit à une augmentation du taux de croissance pour les petits nombres d’onde ainsi que du nombre de Markstein, et à une diminution du taux de croissance pour les grands nombres, du fait des effets des pertes thermiques. / Premixed combustion has been the subject of extensive work, concerning both applications and fundamental aspects. Although in most practical applications combustion occurs in a turbulent environment, the study of laminar flames is important to understand the fundamental mechanisms of turbulent flame propagation. The objective of this work is to study the various instabilities acting on a laminar premixed flame for mixtures of propane-air and methane-air, enriched or not with nitrogen. it consists in measuring the linear growth rates of disturbances in a Hele-Shaw burner formed by two glass plates ($150\times50cm$) separated by a thin gap width (2D burner). Using spatially modulated plates with different wavelengths, the linear growth rate of perturbations can be measured even in the presence of the most unstable wavelength. The experimental values of the linear growth rate as a function of wavenumber are fitted by a linear dispersion relation to estimate the Markstein number and the cutoff wavenumber. For a constant equivalence ratio with increasing values of the dilution in oxygen, the cutoff wavenumber grows with the flame velocity and it is becoming more unstable. The cutoff wave number rises also when the equivalence ratio increases for propane-air mixture and decreases for methane-air mixture, in relation to the evolution of thermal diffusive effects. An enlargement in the thickness of the Hele-Shaw cell results in an increase of the growth rate for small wavenumbers thus in the Markstein number, and in a decline in the growth rate for the large wavenumbers, in relation with the effects of heat losses.