scholarly journals Towards a unified theory of fractional and nonlocal vector calculus

2021 ◽  
Vol 24 (5) ◽  
pp. 1301-1355
Author(s):  
Marta D’Elia ◽  
Mamikon Gulian ◽  
Hayley Olson ◽  
George Em Karniadakis
Keyword(s):  
Ad Hoc ◽  
Broad Class ◽  
Anomalous Behavior ◽  
Unified Theory ◽  
Constrained Problems ◽  
Vector Calculus ◽  
Weighted Laplacian ◽  
Classical Vector ◽  
Laplacian Operators ◽  
Special Case

Abstract Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

The Unified Theory of Tubesheet Design - Part III: Comparison with ASME Method and Case Study

2021 ◽  
Author(s):  
Hong-Song Zhu ◽  
Jinguo Zhai ◽  
Guo-Yan Zhou
Keyword(s):  
Heat Exchangers ◽  
Numerical Comparison ◽  
Unified Theory ◽  
Element Analysis ◽  
Theoretical Comparison ◽  
Comparison Results ◽  
Different Types ◽  
Special Case ◽  
Simplified Mechanical Model

Abstract Based on the unified theory of tubesheet (TS) design for fixed TS heat exchangers (HEX), floating head and U-tube HEX presented in Part I and Part II, theoretical and numerical comparisons with ASME method are performed in this paper as Part III. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the unified theory. Numerical Comparison results indicate that predictions given by the unified theory agree well with finite element analysis (FEA), while ASME results are not accurate or not correct. Therefore, it is concluded that the unified theory deals with different types of HEX in equal detail with confidence to predict design stresses.

Trans‐European Party Groupings: Emergence of New and Alignment of Old Parties in the Light of the Direct Elections to the European Parliament

1979 ◽  
Vol 14 (4) ◽  
pp. 455-478 ◽  
Author(s):  
Paul‐H. Claeys ◽  
Nicole Loeb‐Mayer
Keyword(s):  
Political Parties ◽  
Ad Hoc ◽  
European Parliament ◽  
The Other ◽  
European Level ◽  
Or Groups ◽  
Direct Elections ◽  
Special Case ◽  
Domestic Level

TWO QUESTIONS ARISE WHEN CONSIDERING THE CHANGES that might be brought about by direct elections and by developments in the new European Parliament. One concerns institutionalized cooperation between political parties. To what extent can the three existing European party federations – Socialist, Christian Democrat, Liberal – be considered as a step towards the formation of genuine European political parties? Are they anything more than alignments of traditional parties coordinating their action at European level? The other question is related to parties or groups which have not until now created close-knit ad hoc structures. A special case is that of the Communist parties, which have not organized specific links at Communit level. Another problem is raised by non-traditional parties and groups that have in most cases little or no parlia mentary representation at either national or European level. Will some of them take advantage of the European sphere of action to make more impression than they have been able to do at domestic level, in cooperation with similarly oriented partners in other member countries?

A Bi-Directional Reflectance Function for Woven Textiles

1998 ◽  
Author(s):  
Brad Hunting ◽  
Stephen Derby ◽  
Raymond Puffer
Keyword(s):  
Surface Properties ◽  
Broad Class ◽  
Fiber Surface ◽  
Anisotropic Model ◽  
Reflectance Function ◽  
Function Models ◽  
Woven Textile ◽  
Special Case ◽  
Reflectance Data ◽  
Directional Reflectance

Abstract This paper presents a novel bi-directional reflectance function for woven textile substrates. The new reflectance function models a broad class of woven substrates, including substrates with significant anisotropic reflectance. Isotropic behavior is handled as a special case of the anisotropic model. The new model recognizes fiber surface properties, thread geometry, and weave geometry. Experimental reflectance data is presented.

Fragmentation and Coarse-Grained Content

2021 ◽  
pp. 54-77
Author(s):  
Daniel Greco
Keyword(s):  
Possible Worlds ◽  
Ad Hoc ◽  
Model Building ◽  
Coarse Grained ◽  
Coarse Grain ◽  
The Relationship ◽  
Special Case

This chapter defends the possible worlds framework for modeling the contents of belief. Both the threats against which the chapter defends it—the problems of coarse grain—and the ‘fragmentationist’ response it offers are familiar. At least as a sociological matter, the fragmentationist response has been unpersuasive, likely because it can look like an ad hoc patch—an unmotivated epicycle aimed at saving a flailing theory from decisive refutation. The chapter offers two responses to this charge. First, the problems of coarse grain aren’t unique to the possible worlds framework and indeed arise for anyone who accepts certain very attractive views about the relationship between beliefs, desires, and action. Second, the fragmentationist response to these problems is in fact a special case of an independently motivated, ‘modest’ approach to model-building in philosophy.

Occasionalism and the Cartesian Metaphysic of Motion*

1975 ◽  
Vol 1 (1) ◽  
pp. 29-40 ◽  
Author(s):  
T. M. Lennon
Keyword(s):  
Body Problem ◽  
Ad Hoc ◽  
Body Interaction ◽  
General Account ◽  
Causal Connections ◽  
Mind Body Problem ◽  
The Mind ◽  
Special Case

Occasionalism is often taken by historians of philosophy to have been an ad hoc hypothesis to establish the mind-body causal connections which on Cartesian principles are thought otherwise impossible. My aim in this paper is to show that this view is utterly without historical foundation, that, on the contrary, the view that only God can be a real cause of mind-body interaction was but a special case of a claim argued on grounds transcending the mind-body problem, and, what will be part of this, that the logical character of occasionalism anyhow precluded it from the role into which it was later miscast. More specifically, I shall show that occasionalism was but a consequence of the metaphysics adopted by the Cartesians in their general account of change. Though the same case could be made for the views of Clauberg and Geulincx, my concern will be with the occasionalism of Malebranche. My case here will be that his view is the historical and logical dénouement of principles more or less explicit both in Descartes and in two of his lesser known disciples, LaForge and Cordemoy.

Research and Simulation of Routing Protocol in Different VANET Scenarios

2011 ◽  
Vol 217-218 ◽  
pp. 451-456
Author(s):  
Meng Jun Tong ◽  
Li Yu ◽  
Chang Heng Shu ◽  
Qi Fen Dong ◽  
Feng Gao
Keyword(s):  
Routing Protocol ◽  
Traffic Management ◽  
Ad Hoc ◽  
Road Traffic ◽  
Simulation Software ◽  
Ad Hoc Routing ◽  
Scenarios Simulation ◽  
Stable Performance ◽  
Set Up ◽  
Special Case

VANET is a special case of MANET , and will play an increasingly important role in road traffic management. VANET networks have different motion characters in different scenarios. Through the extension of the current network simulation software NS2, the different simulation scenarios were set up. Several typical Ad hoc routing protocols were simulated and analyzed in the streets and highways scenarios. Simulation results show that AODV and DSR have a relatively stable performance. The results have value in the research and application of VANET to traffic management.

scholarly journals Enhancing the Performance of DSR Routing Protocol Using Link Breakage Prediction in Vehicular Ad Hoc Network

2013 ◽  
Vol 1 (2013) ◽  
pp. 7-14 ◽  
Keyword(s):  
Routing Protocol ◽  
Ad Hoc Network ◽  
Ad Hoc ◽  
Mobile Ad Hoc Network ◽  
High Mobility ◽  
Vehicular Ad Hoc Network ◽  
High Data ◽  
Dynamic Topology ◽  
Dynamic Source ◽  
Special Case

Vehicular Ad hoc Network (VANET) is a special case of Mobile Ad hoc Network (MANET) with two key differences which are the high and constrained mobility of its nodes. Because of this high mobility, the topology of VANET is considered so dynamic. As a reason of this highly dynamic topology, the link breakages in these networks are something common. This problem causes high data loss and delay. In order to decrease these problems, the idea of link breakage prediction has appeared to deal with this phenomenon in MANET. This idea has proved to be successful to enhance the performance of routing protocols in MANET, but till now it did not be applied to the area of VANET. In this paper the idea of link breakage prediction was used to enhance the performance of the well known Dynamic Source Routing protocol (DSR) in VANET by applying a new mechanism which includes replacing the whole effected route (Not only the effected link). This new mechanism was able to decrease the packet loss and delay that occur in the original protocol

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