scholarly journals A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
T. S. Jang ◽  
Hong Gun Sung ◽  
Jinsoo Park
Keyword(s):  
Inverse Problem ◽  
Water Waves ◽  
Solution Procedure ◽  
Solution Stability ◽  
Sea Bottom ◽  
Present Solution ◽  
Ill Posed ◽  
Underwater Movement ◽  
Stabilization Technique

This paper presents an inverse problem and its solution procedure, which are aimed at identifying a sudden underwater movement of the sea bottom. The identification is mathematically shown to work with a known snapshot data of generated water wave configurations. It is also proved that the problem has a unique solution. However, the inverse problem is involved in an integral equation of the first kind, resulting in an ill-posed problem in the sense of stability. That is, the problem lacks solution stability properties. To overcome the difficulty of solution instability, in this paper, a stabilization technique, called regularization, is incorporated in the present solution procedure for the identification of the sea bottom movement. A numerical experiment is presented to demonstrate that the proposed (numerical) solution procedure operates.

scholarly journals Determination of conductivity in a heat equation

2000 ◽  
Vol 24 (9) ◽  
pp. 589-594 ◽  
Author(s):  
Ping Wang ◽  
Kewang Zheng
Keyword(s):  
Numerical Simulation ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Heat Equation ◽  
Ill Posed ◽  
Smooth Data

We consider the problem of determining the conductivity in a heat equation from overspecified non-smooth data. It is an ill-posed inverse problem. We apply a regularization approach to define and construct a stable approximate solution. We also conduct numerical simulation to demonstrate the accuracy of our approximation.

scholarly journals INVERSE PROBLEM OF A ONE-DIMENSIONAL MODEL IN MULTILAYER HEAT CONDUCTION

2020 ◽  
Vol 19 (1) ◽  
pp. 42
Author(s):  
G. C. Oliveira ◽  
S. S. Ribeiroa ◽  
G. Guimarães
Keyword(s):  
Inverse Problem ◽  
Measurement Errors ◽  
Input Data ◽  
Temperature Measurements ◽  
Dimensional Model ◽  
One Dimensional ◽  
Ill Posed ◽  
Measurements Errors ◽  
Chip Chip

The inverse problem in conducting heat is related to the determination of the boundary condition, rate of heat generation, or thermophysical properties, using temperature measurements at one or more positions of the solid. The inverse problem in conducting heat is mathematically one of the ill-posed problems, because its solution extremely sensitive to measurement errors. For a well-placed problem the following conditions must be satisfied: the solution must exist, it must be unique and must be stable on small changes of the input data. The objective of the work is to estimate the heat flux generated at the tool-chip-chip interface in a manufacturing process. The term "estimation" is used because in the temperature measurements, errors are always present and these affect the accuracy of the calculation of the heat flow.

X-Spectrum Determination Applied to Flash Radiography

1991 ◽  
Vol 35 (B) ◽  
pp. 1091-1095
Author(s):  
Loïc Le dain ◽  
Jean-Marc Dinten
Keyword(s):  
Inverse Problem ◽  
Cross Validation ◽  
Maximum Energy ◽  
Direct Measure ◽  
X Ray ◽  
Smoothness Constraint ◽  
Ill Posed ◽  
Validation Technique ◽  
Automatic Choice

AbstractWe propose a method, by absorption [1,2,3,4], of determination of the X-ray spectrum emitted by a flash X-ray radiography generator. This approach leads to an ill posed inverse problem very sensitive to the measures precision.We improve the robustness of the method by introduction of a smoothness constraint on the X-ray spectrum to reconstruct. We also propose an automatic choice of the weight between the measurement and the constraint by using a cross-validation technique.We present an application on an unusual flash X-ray radiography generator - i.e. 75 ns of duration pulse, 6.5 MeV of maximum energy, 350 Rad for dose - for which an instrument of direct measure has not yet been found.

scholarly journals Determination of a power density by an entropy regularization method

2005 ◽  
Vol 2005 (2) ◽  
pp. 127-152 ◽  
Author(s):  
Olivier Prot ◽  
Maïtine Bergounioux ◽  
Jean Gabriel Trotignon
Keyword(s):  
Inverse Problem ◽  
Electromagnetic Field ◽  
Electromagnetic Wave ◽  
Power Density ◽  
Regularization Method ◽  
Power Density Distribution ◽  
Numerical Examples ◽  
Finite Dimensional ◽  
Ill Posed

The determination of directional power density distribution of an electromagnetic wave from the electromagnetic field measurement can be expressed as an ill-posed inverse problem. We consider the resolution of this inverse problem via a maximum entropy regularization method. A finite-dimensional algorithm is derived from optimality conditions, and we prove its convergence. A variant of this algorithm is also studied. This second one leads to a solution which maximizes entropy in the probabilistic sense. Some numerical examples are given.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

Optimum HPLC Conditions for Determination of Dibucaine HCL, Fluocortolone Pivalate and Fluocortolone Caproate by Using Experimental Design

2018 ◽  
Vol 15 (1) ◽  
pp. 32-38 ◽  
Author(s):  
Bürge Aşçı ◽  
Mesut Koç
Keyword(s):  
Experimental Design ◽  
Flow Rate ◽  
Mobile Phase ◽  
High Performance ◽  
Limit Of Detection ◽  
Pharmaceutical Preparations ◽  
Acid Mixture ◽  
Solution Stability ◽  
Uv Detector

Introduction:This paper presents the development and validation of a novel, fast, sensitive and accurate high performance liquid chromatography (HPLC) method for the simultaneous quantitative determination of dibucaine HCl, fluocortolone pivalate and fluocortolone caproate in pharmaceutical preparations.Experiment:Development of the chromatographic method was based on an experimental design approach. A five-level-three-factor central composite design requiring 20 experiments in this optimization study was performed in order to evaluate the effects of three independent variances including mobile phase ratio, flow rate and amount of acid in the mobile phase.Conclusion:The optimum composition for mobile phase was found as a methanol:water:acetic acid mixture at 71.6 : 26.4 : 2 (v/v/v) ratio and optimum separation was acquired by isocratic elution with a flow rate of 1.3 mL/min. The analytes were detected using a UV detector at 240 nm. The developed method was validated in terms of linearity, precision, accuracy, limit of detection/quantitation and solution stability and successfully applied to the determination of dibucaine HCl, fluocortolone pivalate and fluocortolone caproate in pharmaceutical topical formulations such as suppositories and ointments.

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

Resonant reflection of surface water waves by periodic sandbars

1985 ◽  
Vol 152 ◽  
pp. 315-335 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Resonance Condition ◽  
Nonlinear Effects ◽  
Sea Bottom ◽  
Strong Reflection ◽  
Weak Reflection ◽  
Surface Water Waves ◽  
Wave Induced ◽  
Incident Waves ◽  
Resonant Reflection

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.

Sign in / Sign up

Export Citation Format

Share Document