scholarly journals A geometric representation of fragmentation processes on stable trees

2021 ◽  
Vol 49 (5) ◽  
Author(s):  
Paul Thévenin
Keyword(s):  
Geometric Representation ◽  
Fragmentation Processes

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

Representing wine concepts: A hybrid approach

2020 ◽  
Vol 15 (4) ◽  
pp. 475-491
Author(s):  
M. Cristina Amoretti ◽  
Marcello Frixione
Keyword(s):  
Hybrid Approach ◽  
Sufficient Conditions ◽  
Geometric Representation ◽  
Conceptual Spaces ◽  
Geographical Indication ◽  
Knowledge Based ◽  
Quality Dimensions ◽  
Grape Varieties ◽  
Degree Of Similarity ◽  
Representation Of Knowledge

Wines with geographical indication can be classified and represented by such features as designations of origin, producers, vintage years, alcoholic strength, and grape varieties; these features allow us to define wines in terms of a set of necessary and/or sufficient conditions. However, wines can also be identified by other characteristics, involving their look, smell, and taste; in this case, it is hard to define wines in terms of necessary and/or sufficient conditions, as wine concepts exhibit typicality effects. This is a setback for the design of computer science ontologies aiming to represent wine concepts, since knowledge representation formalisms commonly adopted in this field do not allow for the representation of concepts in terms of typical traits. To solve this problem, we propose to adopt a hybrid approach in which ontology-oriented formalisms are combined with a geometric representation of knowledge based on conceptual spaces. As in conceptual spaces, concepts are identified in terms of a number of quality dimensions. In order to determine those relevant for wine representation, we use the terminology developed by the Italian Association of Sommeliers to describe wines. This will allow us to understand typicality effects about wines, determine prototypes and better exemplars, and measure the degree of similarity between different wines.

scholarly journals On the geometrical representation of the powers of quantities, whose indices involve the square roots of negative quantities

1833 ◽  
Vol 2 ◽  
pp. 382-382
Keyword(s):  
General Result ◽  
Geometric Representation ◽  
Square Roots ◽  
Geometrical Representation

The author, in a former paper, read to the Society in February last, had discussed various objections which had been raised against his mode of geometric representation of the square roots of negative quantities. At that time he had only discovered geometrical repre­sentations for quantities of the form a + b √‒1, of geometrically adding and multiplying such quantities, and also of raising them to powers either whole or fractional, positive or negative; but he was at that time unable to represent geometrically quantities raised to powers, whose indices involve the square roots of negative quantities (such as a + b √‒1 m + n ). His attention has since been drawn to this latter class of quantities by a passage in M. Mourey’s work on this subject, which implied that that gentleman was in posses­sion of methods of representing them geometrically, but that he was at present precluded by circumstances from publishing his discoveries. The author was therefore induced to pursue his own investigations, and arrived at the general result stated by M. Mourey, that all algebraic quantities whatsoever are capable of geometrical representation by lines all situated in the same plane. The object of the present paper is to extend the geometrical representations stated in his former treatise, to the powers of quantities, whose indices involve the square roots of negative quantities. With this view he investigates Various equivalent formulæ suited to the particular cases, and employs a peculiar notation adapted to this express purpose ; but the nature of these investigations is such as renders them incapable of abridgement.

scholarly journals Ash from the Eyjafjallajökull eruption (Iceland): Fragmentation processes and aerodynamic behavior

2012 ◽  
Vol 117 (B9) ◽  
Author(s):  
P. Dellino ◽  
M. T. Gudmundsson ◽  
G. Larsen ◽  
D. Mele ◽  
J. A. Stevenson ◽  
...  
Keyword(s):  
Fragmentation Processes

Controllability Ellipsoid to Evaluate the Performance of Mobile Manipulators for Manufacturing Tasks

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Stephen L. Canfield ◽  
Reabetswe M. Nkhumise
Keyword(s):  
Time Domain ◽  
Controller Design ◽  
Control Design ◽  
Quantitative Measure ◽  
Space Representation ◽  
System Response ◽  
Geometric Representation ◽  
Mobile Manipulators ◽  
Control Parameters ◽  
The Time Domain

This paper develops an approach to evaluate a state-space controller design for mobile manipulators using a geometric representation of the system response in tool space. The method evaluates the robot system dynamics with a control scheme and the resulting response is called the controllability ellipsoid (CE), a tool space representation of the system’s motion response given a unit input. The CE can be compared with a corresponding geometric representation of the required motion task (called the motion polyhedron) and evaluated using a quantitative measure of the degree to which the task is satisfied. The traditional control design approach views the system response in the time domain. Alternatively, the proposed CE views the system response in the domain of the input variables. In order to complete the task, the CE must fully contain the motion polyhedron. The optimal robot arrangement would minimize the total area of the CE while fully containing the motion polyhedron. This is comparable to minimizing the power requirements of robot design when applying a uniform scale to all inputs. It will be shown that changing the control parameters changes the eccentricity and orientation of the CE, implying a preferred set of control parameters to minimize the design motor power. When viewed in the time domain, the control parameters can be selected to achieve desired stability and time response. When coupled with existing control design methods, the CE approach can yield robot designs that are stable, responsive, and minimize the input power requirements.

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