arXiv subjects

Costas J. Efthimiou

Publications and source records attributed to Costas J. Efthimiou.

15 recordsLinked to original sources

arXiv2022

The Voronoi Diagram in Soccer: a theoretical study to measure dominance space

In this article, I argue that the concept of the standard Voronoi diagram is incorrect for the calculation of dominance area in soccer. The correct region that should replace the polygonal Voronoi region controlled by a player emerges naturally by studying the motion of the players. It turns out that the widely-used standard Voronoi diagram is true only when all 22 players have the same speed (with vanishing speed being a special case) and it should be replaced by other diagrams whose regions have more complicated boundaries. The unfortunate error happened when the mathematical concept of the Voronoi diagram that has an implicit vanishing speed for its points was transferred to soccer without looking at the kinematical issues involved in the game of soccer. For this reason, as a byproduct of this work, I argue for the promotion of "soccerdynamics", model building for soccer by looking at the underlying mechanisms and not just adopting mathematical ideas only for their appeal and beauty.

physics.soc-ph↗

arXiv2022

A physics-driven study of dominance space in soccer

In arXiv:2107.05714 the concept of the Voronoi diagram was investigated closely from a theoretical point of view. Then, a physics-driven kinematical method was introduced to produce an improved model for dominance space in soccer. Remaining faithful to the deterministic approach, we extend the original work by the introduction of (a) an asymmetric influence of the players in their surrounding area, (b) the frictional forces to the players' motion, and (c) the simultaneous combination of both effects. The asymmetric influence is fairly intuitive; players have more control in the direction they are running than any other direction. The sharper the turn they must make to reach a point on the pitch, the weaker their control of that point will be. From simple kinematical laws, this effect can be quantified explicitly. For the frictional force, a portion comes from air resistance, and so will be proportional to the square of the player's speed, as is well known from fluid dynamics. There are no other external frictional forces, but, at the suggestion of biokinematics, there is an internal frictional force, relating to the consumption of energy by the muscles, which is proportional to the player's speed. Although these additions are intuitively understood, mathematically they introduce many analytical complexities. We establish exact analytical solutions of the dominance areas of the pitch by introducing a few reasonable simplifying assumptions. Given these solutions the new Voronoi diagrams are drawn for the publicly available data by Metrica Sports. In general, it is not necessary anymore for the dominance regions to be convex, they might contain holes, and may be disconnected. The fastest player may dominate points far away from the rest of the players.

physics.soc-ph↗

arXiv2013

Stringy Corrections to the Classical Tests of General Relativity

String theory imposes modifications to Einstein's equations of classical general relativity. Consequently, we calculate the additional corrections to the classical tests: the perihelion precession of Mercury, the deflection of light rays by the sun, and the gravitational redshift which should be present if these modified equations hold. In each case, we determine --- quite consistently with expectations --- that the stringy effects are much too small to be measured.

hep-th↗

arXiv2012

A Class of Continued Radicals

We compute the limits of a class of continued radicals extending the results of a previous note in which only periodic radicals of the class were considered.

math.CA↗

arXiv2012

A Class of Periodic Continued Radicals

We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials.

math.CA↗

arXiv2012

Spherical Harmonics in p Dimensions

The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before beginning the main subject matter. The reader is assumed to have knowledge of multivariable calculus and linear algebra as well as some level of comfort with reading proofs.

math.CA↗

arXiv2008

Putnam Physics Competition: a suggestion

I bring to the attention of the physics community the non-existence of a Putnam Physics Competition in North America despite the fact that the Putnam Mathematical Competition has been well known and highly successful for 70 years.

physics.ed-ph↗

arXiv2007

On the Use of Integrals to Evaluate Series of Rational Terms

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series that generalize a problem published in `The College Mathematics Journal'. Some of the results thus obtained have not been founded in standard references.

math.CA↗

arXiv2005

The Ascending Double-Cone: A Closer Look at a Familiar Demonstration

The double-cone ascending an inclined V-rail is a common exhibit used for demonstrating concepts related to center-of-mass in introductory physics courses. While the conceptual explanation is well-known--the widening of the ramp allows the center of mass of the cone to drop, overbalancing the increase in altitude due to the inclination of the ramp--there remains rich physical content waiting to be extracted through deeper exploration. Such an investigations seems to be absent from the literature. This article seeks to remedy the omission.

physics.class-ph↗

arXiv2004

Cinema as a tool for science literacy

A project known as "Physics in Films" currently underway at UCF is designed to generate renewed interest and excitement in the standard "Physical Science" course. In the initial, developmental phase of the project the instructors selected films without regard to genre and theme. They only demanded that the selected films would cover nearly all the traditional topics of the typical "Physical Science" course. The project met with unprecedented success that motivated a rapid and more sophisticated expansion. In the current phase the authors demonstrate that the method is very flexible, accommodating the movie preferences of any instructor. The authors are developing versions of the course that have different "flavors", that is, "Physics in Films" course packages built around particular genres or themes. For example, during the 2003 summer terms we class-tested the flavors "Physics in Films: Superheroes" and "Physics in Films: Pseudoscience". Additional flavors are under development. This talk summarizes part of our experiences and presents some of the results from our courses. Overall, the method opens an effective way to help large masses to overcome science illiteracy.

physics.pop-ph↗

arXiv2004

Physics in Films: A New Approach to Teaching Science

Over the past year and a half we have developed an innovative approach to the teaching of `Physical Science', a general education course typically found in the curricula of nearly every college and university. The new approach uses popular movies to illustrate the principles of physical science, analyzing individual scenes against the background of the fundamental physical laws. The impact of being able to understand why, in reality, the scene could or could not have occurred as depicted in the film, what the director got right and what he got wrong, has excited student interest enormously in a course that, when taught in the traditional mode, is usually considered to be `too hard and boring'. The performance of students on exams reflected the increased attention to and retention of basic physical concepts, a result that was a primary goal of the `Physics in Films' approach. Following the first offering of the revitalization of the Physical Science course, in which action and sci-fi films were the primary source of the scene clips used in class, the instructors have demonstrated the versatility of the approach by building variations of the course around other genres, as well --`Physics in Films: Superheroes' and `Physics in Films: Pseudoscience'. A parallel approach to the general education course in astronomy is currently being discussed; many others are in our thoughts.

physics.ed-ph↗

arXiv2002

A Mechanism for Charge Quantization

We analyze a potential that produces background charges which are automatically quantized. This introduces a new mechanism for charge quantization, although so far it has only been implemented for background charges. We show that this same mechanism can also lead to an alternative means of hiding extra dimensions that is analogous to the Kaluza-Klein approach.

hep-th↗

arXiv1998

On the Integrability of the Bukhvostov-Lipatov Model

The integrability of the Bukhvostov-Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary actions. It is then established that the conservation law is spoiled at the quantum level -- a fact that might indicate that the quantum Bukhvostov-Lipatov model is not integrable, contrary to what was previously believed.

hep-th↗

arXiv1998

Is the classical Bukhvostov-Lipatov model integrable? A Painlevé analysis

In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlevé analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model. We are led to the conclusion that the model is not integrable classically, except at a trivial point where the theory can be described in terms of two uncoupled sine-Gordon models.

solv-int↗

arXiv1995

Integrable Models on Hyper-Elliptic Surfaces

We present an elementary introduction to the construction of integrable models on hyper-elliptic surfaces for non specialists; also, we present some of the details of the paper `solv-int/9504002' for the more interested readers. (Based on a talk given at the MRST 95 meeting by C. E.)

solv-int↗