Parallel Algorithm for the Local Variations Method

Димитър С. Илиев, Станимир Д. Илиев - Актуално е изследването на поведението на течен менискус в околността на хетерогенна стена. До сега няма получено числено решение за формата на менискуса около стена, която е с хаотична хетерогенност. В настоящата статия е разработен алгоритъм за метода на локалните вариации, който може да се използва на многопроцесорни системи. С този метод е получен за първи път профила на равновесен течен менискус около вертикална стена с хаотична хетерогенност.

Relationship between Changes in Cash Flow and Investments in Publicy Traded Restaurant Firms in the United States

This research investigated the relationship between investments in fixed assets and free cash flows of U.S. restaurant firms while controlling for future investment opportunities and financial constraints. It also investigated investment and cash-flow sensitivity in the context of economic conditions. Results suggested that investments in small firms (with higher financial constraints) had relatively weaker sensitivity to cash flows than investments in large firms (with higher sensitivity). Controlling for economic conditions did not significantly change results. While the debate over sensitivity of investments to cash flows remains unresolved, it has not been explored widely in industry contexts, especially in services such as the restaurant industry. In addition to its contribution to this literature, this paper provides implications for cash-flow management in publicly traded restaurant companies.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

Sydenham Street Revived: A Public Space Experiment

In 2015, the Sydenham Street Revived pop-up park project (SSR) transformed Sydenham Street between Princess and Queen Streets into a temporary pedestrian-only public space. The goal of the project was to test out the idea of permanently pedestrianizing this street section. But what did this urban experiment ultimately prove? Using video footage, photographs, and observations recorded before and during the project, this report analyzes the use of the space in order to evaluate the claim that SSR created a successful public space and to make recommendations for a permanent public space on Sydenham Street. Two research methods were used: quantitative data collection, consisting of headcounts of both pedestrians and stationary users of the space; and a qualitative observational survey, based on the criteria for successful public spaces developed by the Project for Public Spaces. Data collection occurred two days one week prior to the project, and two days during the project, on days that were similar in terms of temperature and weather. The research revealed that the SSR did create a successful public space, although additional research is needed in order to determine how the space would function as a public place throughout different seasons, to study the street closure’s impact on surrounding residents and businesses, and to understand how private commercial activity would influence use. Recommendations for a permanent public space on Sydenham Street include considerations for flexible street design and a continuous, barrier-free surface; ensuring that there is an abundance of places to sit; making opportunities for public and community-created art; and to improve walkability by connecting the grid using a mid-block walkway.

Air Entrainment in the Turbulent Ship Hull Boundary Layer

Turbulent fluctuations in the vicinity of the water free surface along a flat, vertically oriented surface-piercing plate are studied experimentally using a laboratory-scale experiment. In this experiment, a meter-wide stainless steel belt travels horizontally in a loop around two rollers with vertically oriented axes, which are separated by 7.5 meters. This belt device is mounted inside a large water tank with the water level set just below the top edge of the belt. The belt, rollers, and supporting frame are contained within a sheet metal box to keep the device dry except for one 6-meter-long straight test section between rollers. The belt is launched from rest with an acceleration of up to 3-g in order to quickly reach steady state velocity. This creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer created along a flat-sided ship moving at the same velocity, with a length equivalent to the length of belt that has passed the measurement region since the belt motion began. Surface profile measurements in planes normal to the belt surface are conducted using cinematic Laser Induced Fluorescence and quantitative surface profiles are extracted at each instant in time. Using these measurements, free surface fluctuations are examined and the propagation behavior of these free surface ripples is studied. It is found that free surface fluctuations are generated in a region close to the belt surface, where sub-surface velocity fluctuations influence the behavior of these free surface features. These rapidly-changing surface features close to the belt appear to lead to the generation of freely-propagating waves far from the belt, outside the influence of the boundary layer. Sub-surface PIV measurements are performed in order to study the modification of the boundary layer flow field due to the effects of the water free surface. Cinematic planar PIV measurements are performed in horizontal planes parallel to the free surface by imaging the flow from underneath the tank, providing streamwise and wall-normal velocity fields. Additional planar PIV experiments are performed in vertical planes parallel to the belt surface in order to study the bahvior of streamwise and vertical velocity fields. It is found that the boundary layer grows rapidly near the free surface, leading to an overall thicker boundary layer close to the surface. This rapid boundary layer growth appears to be linked to a process of free surface bursting, the sudden onset of free surface fluctuations. Cinematic white light movies are recorded from beneath the water surface in order to determine the onset location of air entrainment. In addition, qualitative observations of these processes are made in order to determine the mechanisms leading to air entrainment present in this flow.

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.

What Is a Firm’s Life Expectancy? Empirical Evidence in the Context of Portuguese Companies

It is a fact that the uncertainty about a firm’s future has to be measured and incorporated into a company’s valuation throughout the explicit analysis period – in the continuing or terminal value within valuation models. One of the concerns that can influence the continuing value of enterprises, which is not explicitly considered in traditional valuation models, is a firm’s average life expectancy. Although the literature has studied the life cycle of a firm, there is still a considerable lack of references on this topic. If we ignore the period during which a company has the ability to produce future cash flows, the valuations can fall into irreversible errors, leading to results markedly different from market values. This paper aims to provide a contribution in this area. Its main objective is to construct a mortality table for non-listed Portuguese enterprises, showing that the use of a terminal value through a mathematical expression of perpetuity of free cash flows is not adequate. We provide the use of an appropriate coefficient to perceive the number of years in which the company will continue to operate until its theoretical extinction. If well addressed regarding valuation models, this issue can be used to reduce or even to eliminate one of the main problems that cause distortions in contemporary enterprise valuation models: the premise of an enterprise’s unlimited existence in time. Besides studying the companies involved in it, from their existence to their demise, our study intends to push knowledge forward by providing a consistent life and mortality expectancy table for each age of the company, presenting models with an explicitly and different survival rate for each year. Moreover, we show that, after reaching a certain age, firms can reinvent their business, acquiring maturity and consequently postponing their mortality through an additional life period.

O valor terminal ou de continuidade, na avaliação de empresas

É um facto que a incerteza sobre o futuro das sociedades tem de ser modelada e incorporada na sua avaliação, fora do período explícito de análise, ou seja: nos valores de continuidade (VC), valor residual (VR) ou valor terminal (VT), considerados nos modelos de avaliação. Existem inúmeros fatores que influenciam o valor de continuidade das empresas e que não são, atualmente, considerados nos modelos de avaliação de empresas, destacando-se, entre os mais relevantes, a ausência de quaisquer referências à esperança média de vida das empresas. De facto, ao ignorarmos esses fatores, podemos incorrer em erros irreparáveis, conduzindo as avaliações a valores de goodwill ou badwill, muito longe do real valor substancial dos ativos, que lhes é intrínseco. Como consequência, os referidos resultados apresentar-se-ão vincadamente diferentes dos valores de mercado. Assim, porque não considerar modelos alternativos (incorporando nos mesmos a esperança de vida das empresas) e a influência de outros fatores, de forma a obter um ajustamento mais eficiente, no que respeita à forma de cálculo do valor da empresa? Este trabalho pretende fornecer um contributo neste domínio, tendo como primeiro objetivo (e para além da revisão da literatura existente sobre a matéria) a construção de uma tábua de mortalidade para as empresas portuguesas, que possa ser utilizada para eliminar ou, pelo menos, reduzir um dos principais problemas causadores de distorção dos atuais modelos de avaliação de empresas: a premissa de existência (ilimitada no tempo) de uma empresa. Com esse propósito, através da metodologia associada à construção de tábuas de mortalidade para os seres humanos, construímos uma tabela com a esperança média de vida associada às empresas portuguesas. Assim, usando uma base de dados (com cerca de 182.000 registos sobre falências, dissoluções e cessão de atividade em Portugal, desde 1900 até 2009), concluímos que, nos primeiros 5 anos, “morrem” 31% das empresas e que a esperança média de vida (à nascença) é de 12 anos. Estes resultados evidenciam a fragilidade dos modelos de avaliação de empresas, em que se estima o VT com uma perpetuidade. Após ficar patente que as empresas não têm uma esperança de vida infinita, preocupar-nos-emos em identificar quais os fatores responsáveis pela existência da empresa (no longo prazo), fatores esses que possam, porventura, justificar uma vida mais longa das sociedades. VI Nesse sentido, o segundo objetivo passou por identificar quais os fatores determinantes do valor terminal da empresa. Assim [utilizando uma amostra de 714 empresas cotadas, pertencentes a 15 países europeus e para um período compreendido entre 1992 e 2011, usando a metodologia GMM (Generalized method of moments), aplicada a dados em painel dinâmico], os resultados evidenciam que o valor de continuidade não pode ser considerado como o valor atual de uma perpetuidade constante (ou com crescimento) de um determinado atributo da empresa mas, sim, em função de um conjunto de atributos, como os free cash flows, os resultados líquidos, a esperança média de vida da empresa, o investimento em I&D, as capacidades e qualidade da gestão, a liquidez dos títulos e a estrutura de financiamento. Como terceiro objetivo (e mantendo a particular atenção na estimação do VT da empresa), procurou-se cruzar os resultados obtidos no estudo anterior com as perceções dos analistas Europeus e Estadunidenses acerca dos atributos da empresa que, na opinião destes, mais contribuem para o seu valor. Para o feito, recorreu-se a um inquérito, com respostas fechadas. Da análise das 123 respostas válidas, obtidas usando a análise fatorial, concluiuse serem determinantes do valor de uma empresa ou negócio os seguintes fatores: a esperança média de vida da empresa, a sua liquidez e desempenho operacional, a inovação e capacidade de afetação de recursos a I&D, as capacidades de gestão e a estrutura de capital, confirmando-se as conclusões até então obtidas. Por fim, fez-se um esforço no sentido de fornecer ao leitor uma nova aproximação teórica ao modelo Discounted CashFlow (DCF), tendo em conta as variáveis entretanto identificadas no nosso estudo. Estes resultados contribuem, a nosso ver, para que se possa caminhar no sentido da construção de um modelo de avaliação de empresas e negócios ainda mais apurado, em que os resultados obtidos nas avaliações se aproximem o mais possível dos verificados no mercado.

Corner Flows in Free Liquid Films

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x² – y², η = 2xy, applies to films that are thin in the η direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature

The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical flat plate with streamwise sinusoidal surface temperature has been investigated in this study. Using the appropriate variables; the basic governing equations are transformed to convenient form and then solved numerically employing two efficient methods, namely, Implicit finite difference method (IFD) together with Keller box scheme and Straight forward finite difference (SFFD) method. Effects of the variation of the physical parameters, for example, conduction-radiation parameter (Planck number), surface temperature parameter, and the amplitude of the surface temperature, are shown on the skin friction and heat transfer rate quantitatively are shown numerically. Velocity and temperature profiles as well as streamlines and isotherms are also presented and discussed for the variation of conduction-radiation parameter. It is found that both skin-friction and rate of heat transfer are enhanced considerably by increasing the values of conduction radiation parameter, Rd.

The effect of the nonparabolicity of the free carriers dispersion law on the propagation of surface polaritons in a semiconductor-metal structure

The results of a study on the influence of the nonparabolicity of the free carriers dispersion law on the propagation of surface polaritons (SPs) located near the interface between an n-type semiconductor and a metal arc reported. The semiconductor plasma is assumed to be warm and nonisothermal. The nonparabolicity of the electron dispersion law has two effects. The first one is associated with nonlinear self-interaction of the SPs. The nonlinear dispersion equation and the nonlinear Schrodinger equation for the amplitude of the SP envelope are obtained. The nonlinear evolution of the SP is studied on the base of the above mentioned equations. The second effect results in third harmonics generation. Analysis shows that these third harmonics may appear as a pure surface polariton, a pseudosurface polariton, or a superposition of a volume wave and a SP depending on the wave frequency, electron density and lattice dielectric constant.

Solutions of Boundary Layer Equations Governing Free Convective and Magnetohydrodynamic Flows through Parametric Differentiation

In der vorliegenden Arbeit wird die Methode der parametrischen Differentiation angewendet, um ein System nichtlinearer Gleichungen zu lösen, das zwei- und dreidimensionale freie, konvektive Grenzschichströmungen bzw. eine zweidimensionale magnetohydrodynamische Grenzschichtströmung beherrscht. Der Hauptvorteil dieser Methode besteht darin, daß die nichlinearen Gleichungen auf lineare reduziert werden und die Nichtlinearität auf ein System von Gleichungen erster Ordnung beschränkt wird, das, verglichen mit den ursprünglichen Nichtlinearen Gleichungen, viel leichter gelöst werden kann. Ein anderer Vorzug der Methode ist, daß sie es ermöglicht, die Lösung von einer bekannten, zu einem bestimmten Parameterwert gehörigen Lösung aus durch schrittweises Vorgehen die Lösung für den gesamten Parameterbereich zu erhalten. Die mit dieser Methode gewonnenen Ergebnisse stimmen gut mit den entsprechenden, mit anderen numerischen Verfahren erzielten überein.

Material processing and surface reaction studies in free piston driven shock tube

Recently established moderate size free piston driven hypersonic shock tunnel HST3 along with its calibration is described here. The extreme thermodynamic conditions prevalent behind the reflected shock wave have been utilized to study the catalytic and non-catalytic reactions of shock heated test gases like Ar, N2 or O2 with different material like C60 carbon, zirconia and ceria substituted zirconia. The exposed test samples are investigated using different experimental methods. These studies show the formation of carbon nitride due to the non-catalytic interaction of shock heated nitrogen gas with C60 carbon film. On the other hand, the ZrO2 undergoes only phase transformation from cubic to monoclinic structure and Ce0.5Zr0.5O2 in fluorite cubic phase changes to pyrochlore (Ce2Zr2O7±δ) phase by releasing oxygen from the lattice due to heterogeneous catalytic surface reaction.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.