Kinematics of accretionary shell growth, with examples from brachiopods and molluscs

Paleobiology ◽  
1989 ◽  
Vol 15 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Spafford C. Ackerly
Keyword(s):  
Inverse Problem ◽  
Reference Frame ◽  
Computer Simulations ◽  
Reference Model ◽  
Shell Growth ◽  
Analytical Framework ◽  
Growth Forms ◽  
Present Position ◽  
Growth Step ◽  
Biological Reality

A moving reference frame is introduced for the analysis of accretionary shell growth. Simple principles of motion and stepwise growth define the model. At each growth step, the aperture migrates from its present position to a new position, according to locally defined rules. The aperture becomes the focus of the analysis, mathematically and conceptually, in conformity with biological reality. Kinematic principles provide the analytical framework for describing the aperture's trajectory (kinematics is the study of motion). The aperture “translates,” “rotates,” and “dilates.” The model offers exceptional flexibility in the analysis of accretionary growth forms and is particularly well-suited to analysis of conical and loosely coiled shell geometries. Computer simulations illustrate the principles of a moving reference model. The inverse problem of finding the aperture motions from actual shell data is rigorously specified, for both planispiralled and helicospiralled shell forms.

Born inversion with a variable background velocity

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1794-1797 ◽  
Author(s):  
Douglas J. Foster ◽  
Philip M. Carrion
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Basic Assumption ◽  
Reference Model ◽  
Born Model

Direct, or Born, inversion has been presented as an approximate solution of the multidimensional seismic‐acoustic inverse problem (e.g., Cohen and Bleistein, 1979; Phinney and Frazer, 1978; Raz, 1981; Clayton and Stolt, 1981). The most basic assumption of the Born model is that variations, or perturbations, of some reference model remain small. This requirement of smallness is due to the fact that errors are directly related to the value of the perturbations. Both the local and overall values of the perturbation variable contribute to these errors, which are reduced if the known reference model, or background velocity, closely matches the actual medium velocity.

scholarly journals Determining the solar structure from oscillation frequencies

1995 ◽  
Vol 10 ◽  
pp. 329-331
Author(s):  
S. Basu
Keyword(s):  
Inverse Problem ◽  
Kinetic Energy ◽  
Unknown Function ◽  
Sound Speed ◽  
Reference Model ◽  
Solar Interior ◽  
Model Parameters ◽  
Surface Layers ◽  
The Difference ◽  
Oscillation Frequencies

The inverse problem of finding the structure of the solar interior from the observed frequencies can be written aswhere, δωi is the difference in frequency of the ith mode between the solar data and the reference model, f1 and f2 are an appropriate pair of model parameters (e.g. sound speed squared c2, and density ρ), Ei is the mode kinetic energy, K(1) and K(2) are known functions of the reference model, and F(ω) is the unknown function added to account for uncertainties associated with the physics of the surface layers.

Focused inversion of vertical radar profile (VRP) traveltime data

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. H9-H18 ◽  
Author(s):  
Giulio Vignoli ◽  
Rita Deiana ◽  
Giorgio Cassiani
Keyword(s):  
Inverse Problem ◽  
Physical Properties ◽  
Reference Model ◽  
A Priori ◽  
S Wave ◽  
Compact Structure ◽  
Arrival Times ◽  
Minimum Support ◽  
Error Amplification ◽  
Zero Offset

The reconstruction of the GPR velocity vertical profile from vertical radar profile (VRP) traveltime data is a problem with a finite number of measurements and imprecise data, analogous to similar seismic techniques, such as the shallow down-hole test used for S-wave velocity profiling or the vertical seismic profiling (VSP) commonly used in deeper exploration. The uncertainty in data accuracy and the error amplification inherent in deriving velocity estimates from gradients of arrival times make this an example of an ill-posed inverse problem. In the framework of Tikhonov regularization theory, ill-posedness can be tackled by introducing a regularizing functional (stabilizer). The role of this functional is to stabilize the numerical solution by incorporating the appropriate a priori assumptions about the geometrical and/or physical properties of the solution. One of these assumptions could be the existence of sharp boundaries separating rocks with different physical properties. We apply a method based on the minimum support stabilizer to the VRP traveltime inverse problem. This stabilizer makes it possible to produce more accurate profiles of geological targets with compact structure. We compare more traditional inversion results with our proposed compact reconstructions. Using synthetic examples, we demonstrate that the minimum support stabilizer allows an improved recovery of the profile shape and velocity values of blocky targets. We also study the stabilizer behavior with respect to different noise levels and different choices of the reference model. The proposed approach is then applied to real cases where VPRs have been used to derive moisture content profiles as a function of depth. In these real cases, the derived sharper profiles are consistent with other evidence, such as GPR zero-offset profiles, GPR reflections and known locations of the water table.

Analysis of the Influence of Fixture Locator Errors on the Compliance of Work Part Features to Geometric Tolerance Specifications

2003 ◽  
Vol 125 (3) ◽  
pp. 609-616 ◽  
Author(s):  
Rodrigo A. Marin ◽  
Placid M. Ferreira
Keyword(s):  
Inverse Problem ◽  
Reference Frame ◽  
Forward Problem ◽  
Acceptable Level ◽  
Geometric Tolerance ◽  
Mechanical Part ◽  
Geometric Tolerances ◽  
Nc Program ◽  
Functional Features ◽  
Position And Orientation

A machining fixture controls position and orientation of datum references (used to define important functional features of the geometry of a mechanical part) relative the reference frame for an NC program. Inaccuracies in fixture’s location scheme result in a deviation of the work part from its nominal specified geometry. For a part to be acceptable this deviation must be within the limits allowed by the geometric tolerances specified. This paper addresses the problem of characterizing the acceptable level of inaccuracy in the location scheme so that the features machined on the part comply with the limits associated with its geometric tolerances. First we solve the “forward problem” that involves predicting the tolerance deviation resulting at a feature from a known set of errors on the locators. However, the paper concentrates on solving the “inverse” problem that involves establishing bounds on the errors of the locators to ensure that the limits specified by geometric tolerances at a feature are not violated.

Speed Sensorless Vector Control of Cascaded Inverter for Asynchronous Motor

2012 ◽  
Vol 241-244 ◽  
pp. 1797-1801
Author(s):  
Qi Yang ◽  
Yu Feng Zhang ◽  
Shi Bao Qian ◽  
Bing Li
Keyword(s):  
Vector Control ◽  
Reference Frame ◽  
Reference Model ◽  
Current Model ◽  
Asynchronous Motor ◽  
Speed Sensorless ◽  
Two Phase ◽  
Sensorless Vector Control ◽  
Rotating Reference Frame ◽  
Rotor Flux

According to speed sensorless vector control of Asynchronous motor for Cascaded high voltage inverter, a model reference adaptive system (MRAS) implemented in two phase rotating reference frame was studied to identify the rotor speed of an asynchronous motor. To eliminate the inherent limitations of MRAS in two phase stationary reference frame, the reference model and adjustable model used in this MRAS scheme are composed of an improved rotor flux voltage model and rotor flux current model in two phase rotating reference frame respectively. Simulation and experimental results show that the vector control system can estimate the flux and speed with good accuracy, and run with good static and dynamic performance in start, speed regulation and steady operation.

scholarly journals Empirical lognormality of biological variation: implications for the ‘zero-force evolutionary law’

2020 ◽  
Author(s):  
Philip D. Gingerich
Keyword(s):  
Random Walk ◽  
Reference Frame ◽  
Analytical Framework ◽  
Biological Variation ◽  
Total Variance ◽  
Additive Arithmetic ◽  
Zero Force ◽  
Statistical Expectation ◽  
Initial Difference ◽  
Zero Force Evolutionary Law

ABSTRACTThe zero-force evolutionary law (ZFEL) of McShea et al. states that independently evolving entities, with no forces or constraints acting on them, will tend to accumulate differences and therefore diverge from each other. McShea et al. quantified the law by assuming normality on an additive arithmetic scale and reflecting negative differences as absolute values, systematically augmenting perceived divergence. The appropriate analytical framework is not additive but proportional, where logarithmic transformation is required to achieve normality. Logarithms and logarithmic differences can be negative but the proportions they represent cannot be negative. Reformulation of ZFEL in a proportional or geometric reference frame indicates that when entities evolve randomly and independently, differences smaller than any initial difference are balanced by differences larger than the initial difference. Total variance increases with each step of a random walk, but there is no statistical expectation of divergence between random-walk lineages.

scholarly journals Inverse Problem of Selection of the Theoretical Cycle for the Real Cycle of Internal Combustion Engine

2019 ◽  
Vol 26 (2) ◽  
pp. 197-204
Author(s):  
Zbigniew Żmudka ◽  
Stefan Postrzednik ◽  
Grzegorz Przybyła
Keyword(s):  
Inverse Problem ◽  
Internal Combustion Engine ◽  
Reference Model ◽  
Combustion Engine ◽  
Direct Determination ◽  
Internal Combustion ◽  
Heat Distribution ◽  
The Real ◽  
Starting Point ◽  
Selection Of

Abstract The effectiveness of work of an internal combustion engine can be assessed by means of the energy efficiency: theoretical, internal and effective... In the problem regarding the efficiency of obtaining a work from the tested SI engine, the theoretical Seiliger-Sabathe cycle was adopted as a reference model for the real engine cycle. For comparison, the OTTO cycle was also analysed. The engine indicating allows direct determination only of internal work. However, determining the work of the theoretical cycle first requires solving the problem of selecting the parameters of the theoretical cycle, according to the real cycle of the engine (inverse problem). In order uniquely to determine the course of the theoretical Seiliger-Sabathe cycle, it is necessary to determine the parameters of the starting point and the heat distribution number. The selection of the theoretical cycle for the real cycle, within the scope of determining the number of heat distribution, is to some extent of a contractual nature. Therefore, the problem of determining the number of heat distribution was solved by two own original methods. A comparison of the real cycle with the theoretical cycle determined for it is presented.

scholarly journals Computer Simulations of Ethics: the Applicability of Agent-Based Modeling for Ethical Theories

2018 ◽  
Vol 2 (2) ◽  
pp. 76
Author(s):  
Jeremiah A. Lasquety-Reyes
Keyword(s):  
Computer Simulation ◽  
Virtue Ethics ◽  
Computer Simulations ◽  
Reference Model ◽  
Real Life ◽  
Agent Based Modeling ◽  
Ethical Theories ◽  
Agent Based ◽  
Deontological Ethics ◽  
Philosophical Ethics

I consider the applicability of Agent-Based Modeling (ABM) and computer simulations for ethical theories. Though agent-based modeling is already well established in the social sciences, it has not yet found acceptance in the field of philosophical ethics. Currently, there are only a few works explicitly connecting ethics with agent-based modeling. In this paper, I show that it is possible to build computer simulations of ethical theories and that there are also potential benefits in doing so: (1) the opportunity for virtual ethical experiments that are impossible to do in real life, and (2) an increased understanding and appreciation of an ethical theory either through the programming implementation or through the visual simulation. In the first part of the paper, I mention some social science simulations with ethical import that could encourage ethicists to work with ABM. Second, I list the few pioneering works that attempt to combine computer simulation with philosophical ethics, the most prominent being Evolving Ethics: The New Science of Good and Evil (2010) by Mascaro et al. Third, I give pointers for the computer simulation of the most prominent ethical theories: deontological ethics, utilitarianism, feminist care ethics, and virtue ethics. In the final part, I consider the potential of using an existing reference model for the simulation of human behavior, the PECS model, as the foundation for a computer simulation of virtue ethics.

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