scholarly journals Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Gian Luigi Gragnani ◽  
Maurizio Diaz Mendez
Keyword(s):  
Closed Form ◽  
Cross Sections ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Computation Time ◽  
Shape Reconstruction ◽  
Form Solution ◽  
Scattering Data ◽  
Equivalent Sources ◽  
Value Decomposition

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time.

Comparison of Static and Dynamic Stiffness for Beams Undergoing Flexural and Torsional Loading With an Intermediate Mass

2000 ◽  
Author(s):  
Arnoldo Garcia ◽  
Arnold Lumsdaine ◽  
Ying X. Yao
Keyword(s):  
Closed Form ◽  
Natural Frequency ◽  
Cross Sections ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Torsional Loading ◽  
Intermediate Mass ◽  
Form Equation

Abstract Many studies have been performed to analyze the natural frequency of beams undergoing both flexural and torsional loading. For example, Adam (1999) analyzed a beam with open cross-sections under forced vibration. Although the exact natural frequency equation is available in literature (Lumsdaine et al), to the authors’ knowledge, a beam with an intermediate mass and support has not been considered. The models are then compared with an approximate closed form solution for the natural frequency. The closed form equation is developed using energy methods. Results show that the closed form equation is within 2% percent when compared to the transcendental natural frequency equation.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

scholarly journals A Closed-form Solution for Source-term Emission of Xenon Isotopes from Underground Nuclear Explosions

2021 ◽  
Author(s):  
Yunwei Sun ◽  
Charles Carrigan ◽  
William Cassata ◽  
Yue Hao ◽  
Souheil Ezzedine ◽  
...  
Keyword(s):  
Closed Form ◽  
Radioactive Decay ◽  
Closed Form Solution ◽  
Compartment Model ◽  
Form Solution ◽  
Isotopic Ratios ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Xenon Isotopes ◽  
Value Decomposition

AbstractIsotopic ratios of radioactive xenons sampled in the subsurface and atmosphere can be used to detect underground nuclear explosions (UNEs) and civilian nuclear reactors. Disparities in the half-lives of the radioactive decay chains are principally responsible for time-dependent concentrations of xenon isotopes. Contrasting timescales, combined with modern detection capabilities, make the xenon isotopic family a desirable surrogate for UNE detection. However, without including the physical details of post-detonation cavity changes that affect radioxenon evolution and subsurface transport, a UNE is treated as an idealized system that is both closed and well mixed for estimating xenon isotopic ratios and their correlations so that the spatially dependent behavior of xenon production, cavity leakage, and transport are overlooked. In this paper, we developed a multi-compartment model with radioactive decay and interactions between compartments. The model does not require the detailed domain geometry and parameterization that is normally needed by high-fidelity computer simulations, but can represent nuclide evolution within a compartment and migration among compartments under certain conditions. The closed-form solution to all nuclides in the series 131–136 is derived using analytical singular-value decomposition. The solution is further used to express xenon ratios as functions of time and compartment position.

scholarly journals Closed form solution in buckling optimization problem of twisted rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Shape ◽  
Actual Problem ◽  
The Cross ◽  
Simply Connected

Abstract The applications of this method for stability problems are illustrated in this manuscript. In the context of twisted rods, the counterpart for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under torsion (Greenhill, 1883). We search the optimal shape of the rod along its axis. A priori form of the cross-section remains unknown. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. Thus, we drop the assumption about the equality of principle moments of inertia for the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The distribution of material along the length of a twisted rod is optimized so that the rod is of the constant volume T and will support the maximal moment without spatial buckling. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. We demonstrate at the beginning the validity of static Euler’s approach for simply supported rod (hinged), twisted by the conservative moment. The applied method for integration of the optimization criteria delivers different length and volumes of the optimal twisted rods. Instead of the seeking for the twisted rods of the fixed length and volume, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for twisted rod is stated in closed form in terms of the higher transcendental functions. In the torsion stability problem, the optimal shape of cross-section is the equilateral triangle.

scholarly journals CHARACTERIZING AND MANAGING AN EPIDEMIC: A FIRST PRINCIPLES MODEL AND A CLOSED FORM SOLUTION TO THE KERMACK AND MCKENDRICK EQUATIONS

2021 ◽  
Author(s):  
Theodore G Duclos ◽  
Thomas A Reichert
Keyword(s):  
Closed Form ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Prima Facie ◽  
Form Solution ◽  
Public Health Decision ◽  
Mobility Data ◽  
Containment Measures ◽  
Two Parameters ◽  
Analytical Tools

We derived a closed-form solution to the original epidemic equations formulated by Kermack and McKendrick in 1927 (1). The complete solution is validated using independently measured mobility data and accurate predictions of COVID-19 case dynamics in multiple countries. It replicates the observed phenomenology, quantitates pandemic dynamics, and provides simple analytical tools for policy makers. Of particular note, it projects that increased social containment measures shorten an epidemic and reduce the ultimate number of cases and deaths. In contrast, the widely used Susceptible Infectious Recovered (SIR) models, based on an approximation to Kermack and McKendricks original equations, project that strong containment measures delay the peak in daily infections, causing a longer epidemic. These projections contradict both the complete solution and the observed phenomenology in COVID-19 pandemic data. The closed-form solution elucidates that the two parameters classically used as constants in approximate SIR models cannot, in fact, be reasonably assumed to be constant in real epidemics. This prima facie failure forces the conclusion that the approximate SIR models should not be used to characterize or manage epidemics. As a replacement to the SIR models, the closed-form solution and the expressions derived from the solution form a complete set of analytical tools that can accurately diagnose the state of an epidemic and provide proper guidance for public health decision makers.

scholarly journals The Missing Link: A Closed Form Solution to the Kermack and McKendrick Model Equations

2021 ◽  
Author(s):  
Theodore G Duclos ◽  
Thomas A Reichert
Keyword(s):  
Closed Form ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Policy Makers ◽  
Mobility Data ◽  
Forward Limit ◽  
Containment Measures ◽  
Model Equations ◽  
Analytical Tools

Susceptible infectious recovered (SIR) models are widely used for estimating the dynamics of epidemics. Such models project that containment measures flatten the curve, i.e., reduce but delay the peak in daily infections, cause a longer epidemic, and increase the death toll. These projections have entered common understanding; individuals and governments often advocate lifting containment measures such as social distancing to shift the peak forward, limit societal and economic disruption, and reduce mortality. It was, then, an extraordinary surprise to discover that COVID-19 pandemic data exhibit phenomenology opposite to the projections of SIR models. With the knowledge that the commonly used SIR equations only approximate the original equations developed to describe epidemics, we identified a closed form solution to the original epidemic equations. Unlike the commonly used approximations, the closed form solution replicates the observed phenomenology and quantitates pandemic dynamics with simple analytical tools for policy makers. The complete solution is validated using independently measured mobility data and accurately predicts COVID19 case numbers in multiple countries.

Efficient Closed-Form Solution of the Kinematics of a Tunnel Digging Machine

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Paolo Boscariol ◽  
Alessandro Gasparetto ◽  
Lorenzo Scalera ◽  
Renato Vidoni
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
Large Size ◽  
Closure Equation ◽  
Class 1 ◽  
Spherical Mechanism ◽  
Kinematic Solution

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

Sign in / Sign up

Export Citation Format

Share Document