High Precision Compact Thermal Models

2005 ◽  
Author(s):  
Mohamed-Nabil Sabry
Keyword(s):  
A Priori ◽  
A Priori Estimate ◽  
Compact Model ◽  
Heat Sources ◽  
New Approach ◽  
Thermal Models ◽  
Common Structure ◽  
Accuracy Level ◽  
Original Approach ◽  
Node Size

This paper is a step towards building a more complete theory of compact thermal models, in which their common structure is highlighted and hence the sources of errors inevitably present in any compact model clearly revealed. This approach is further extended in order to propose an original approach to attain any desired level of precision. Different methods already proposed by other authors can all benefit from the approach proposed here in order to raise accuracy level. Traditionally, increasing precision was attained by increasing the number of nodes. This strategy faces many problems, like the difficulty to select node size and position, as well as the inability to provide an a priori estimate of the number of nodes needed. In particular, this strategy fails in the case of multiple heat sources (MCM). The actual approach relies on a “flexible” pattern model that allows us to avoid such problems. Moreover, the new approach gives access to the tangential temperature gradient. This valuable information for designers in order to assess reliability can not be predicted by classical compact model approaches.

Flexible Profile Compact Thermal Models for Practical Geometries

2007 ◽  
Vol 129 (3) ◽  
pp. 256-259 ◽  
Author(s):  
Mohamed-Nabil Sabry
Keyword(s):  
A Priori ◽  
A Priori Estimate ◽  
Operating Conditions ◽  
Heat Sources ◽  
Order Of Accuracy ◽  
New Approach ◽  
Thermal Models ◽  
Volumetric Heating ◽  
2D Structure ◽  
Node Size

Recent advances in compact thermal models have led to the emergence of a new concept allowing models to be created at any desired order of accuracy. Traditionally, increasing precision was attained by increasing the number of nodes. This strategy faces many problems; in particular, for the case of multiple heat sources (MCM) and∕or stacked dies, because different operating conditions will lead to different temperature and heat flux profiles that will require different node partitioning in order to be matched. In fact, classical approaches face a difficulty in selecting appropriate node size and position, as well as the inability to provide an a priori estimate of the number of nodes needed. The new concept is based on the use of a flexible profile to account for different possible uses of the model. In particular, it can deal with different patterns of heat generation encountered in MCM and stacked dies, and hence it is truly boundary conditions independent. Moreover, the new approach gives access to the tangential temperature gradient. This valuable information for designers in order to assess reliability cannot be predicted by classical compact model approaches. The concept was presented earlier for a simple rectangular 2D structure with surface heating (2004, 10th THERMINIC Conference, pp. 273–280). In this paper, the concept will be generalized to 3D parallelepiped boxes with both surface and∕or volumetric heating. The second achievement is the possibility to deal with geometries that can be decomposed into boxes.

scholarly journals Virtual Sensor for Calibration of Thermal Models of Machine Tools

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander Dementjev ◽  
Burkhard Hensel ◽  
Klaus Kabitzsch ◽  
Bernd Kauschinger ◽  
Steffen Schroeder
Keyword(s):  
Machine Tools ◽  
Model Calibration ◽  
Thermal Deformation ◽  
A Priori ◽  
High Dimensional ◽  
Effective Solution ◽  
Adequate Model ◽  
New Approach ◽  
Thermal Models ◽  
Industrial Manufacturing

Machine tools are important parts of high-complex industrial manufacturing. Thus, the end product quality strictly depends on the accuracy of these machines, but they are prone to deformation caused by their own heat. The deformation needs to be compensated in order to assure accurate production. So an adequate model of the high-dimensional thermal deformation process must be created and parameters of this model must be evaluated. Unfortunately, such parameters are often unknown and cannot be calculated a priori. Parameter identification during real experiments is not an option for these models because of its high engineering and machine time effort. The installation of additional sensors to measure these parameters directly is uneconomical. Instead, an effective calibration of thermal models can be reached by combining real and virtual measurements on a machine tool during its real operation, without additional sensors installation. In this paper, a new approach for thermal model calibration is presented. The expected results are very promising and can be recommended as an effective solution for this class of problems.

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Survey Data Quality in Analyzing Harmonized Indicators of Protest Behavior: A Survey Data Recycling Approach

2021 ◽  
pp. 000276422110216
Author(s):  
Kazimierz M. Slomczynski ◽  
Irina Tomescu-Dubrow ◽  
Ilona Wysmulek
Keyword(s):  
Data Processing ◽  
Data Quality ◽  
Survey Data ◽  
A Priori ◽  
Data Sets ◽  
New Approach ◽  
Survey Quality ◽  
Survey Error ◽  
Ex Post ◽  
The Impact

This article proposes a new approach to analyze protest participation measured in surveys of uneven quality. Because single international survey projects cover only a fraction of the world’s nations in specific periods, researchers increasingly turn to ex-post harmonization of different survey data sets not a priori designed as comparable. However, very few scholars systematically examine the impact of the survey data quality on substantive results. We argue that the variation in source data, especially deviations from standards of survey documentation, data processing, and computer files—proposed by methodologists of Total Survey Error, Survey Quality Monitoring, and Fitness for Intended Use—is important for analyzing protest behavior. In particular, we apply the Survey Data Recycling framework to investigate the extent to which indicators of attending demonstrations and signing petitions in 1,184 national survey projects are associated with measures of data quality, controlling for variability in the questionnaire items. We demonstrate that the null hypothesis of no impact of measures of survey quality on indicators of protest participation must be rejected. Measures of survey documentation, data processing, and computer records, taken together, explain over 5% of the intersurvey variance in the proportions of the populations attending demonstrations or signing petitions.

scholarly journals Positive solutions of higher order quasilinear elliptic equations

2002 ◽  
Vol 7 (8) ◽  
pp. 423-452
Author(s):  
Marcelo Montenegro
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
A Priori Estimate ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
The Maximum Principle ◽  
Priori Estimates ◽  
Quasilinear Elliptic

The higher order quasilinear elliptic equation−Δ(Δp(Δu))=f(x,u)subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.

scholarly journals On the security of $\alpha\eta$: response to 'some attacks on quantum-based cryptographic protocols'

2006 ◽  
Vol 6 (7) ◽  
pp. 561-582
Author(s):  
H.P. Yuen ◽  
R. Nair ◽  
E. Corndorf ◽  
G.S. Kanter ◽  
P. Kumar
Keyword(s):  
Coherent State ◽  
Optical Communications ◽  
A Priori ◽  
Key Generation ◽  
Generation System ◽  
New Approach ◽  
Security Proof ◽  
Grover Search ◽  
Channel Loss ◽  
Key Length

Lo and Ko have developed some attacks on the cryptosystem called $\alpha \eta$}, claiming that these attacks undermine the security of $\alpha\eta$ for both direct encryption and key generation. In this paper, we show that their arguments fail in many different ways. In particular, the first attack in [1] requires channel loss or length of known-plaintext that is exponential in the key length and is unrealistic even for moderate key lengths. The second attack is a Grover search attack based on `asymptotic orthogonality' and was not analyzed quantitatively in [1]. We explain why it is not logically possible to "pull back'' an argument valid only at $n=\infty$ into a limit statement, let alone one valid for a finite number of transmissions n. We illustrate this by a `proof' using a similar asymptotic orthogonality argument that coherent-state BB84 is insecure for any value of loss. Even if a limit statement is true, this attack is a priori irrelevant as it requires an indefinitely large amount of known-plaintext, resources and processing. We also explain why the attacks in [1] on $\alpha\eta$ as a key-generation system are based on misinterpretations of [2]. Some misunderstandings in [1] regarding certain issues in cryptography and optical communications are also pointed out. Short of providing a security proof for $\alpha\eta$, we provide a description of relevant results in standard cryptography and in the design of $\alpha\eta$ to put the above issues in the proper framework and to elucidate some security features of this new approach to quantum cryptography.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

Sign in / Sign up

Export Citation Format

Share Document