Billiard Ball Research Articles

Effective recognition design in 8-ball billiards vision systems for training purposes based on Xception network modified by improved Chaos African Vulture Optimizer

This research paper presents a comprehensive investigation into the utilization of color image processing technologies and deep learning algorithms in the development of a robot vision system specifically designed for 8-ball billiards. The sport of billiards, with its various games and ball arrangements, presents unique challenges for robotic vision systems. The proposed methodology addresses these challenges through two main components: object detection and ball pattern recognition. Initially, a robust algorithm is employed to detect the billiard balls using color space transformation and thresholding techniques. This is followed by determining the position of the billiard table through strategic cropping and isolation of the primary table area. The crucial phase involves the intricate task of recognizing ball patterns to differentiate between solid and striped balls. To achieve this, a modified convolutional neural network is utilized, leveraging the Xception network optimized by an innovative algorithm known as the Improved Chaos African Vulture Optimization (ICAVO) algorithm. The ICAVO algorithm enhances the Xception network's performance by efficiently exploring the solution space and avoiding local optima. The results of this study demonstrate a significant enhancement in recognition accuracy, with the Xception/ICAVO model achieving remarkable recognition rates for both solid and striped balls. This paves the way for the development of more sophisticated and efficient billiards robots. The implications of this research extend beyond 8-ball billiards, highlighting the potential for advanced robotic vision systems in various applications. The successful integration of color image processing, deep learning, and optimization algorithms shows the effectiveness of the proposed methodology. This research has far-reaching implications that go beyond just billiards. The cutting-edge robotic vision technology can be utilized for detecting and tracking objects in different sectors, transforming industrial automation and surveillance setups. By combining color image processing, deep learning, and optimization algorithms, the system proves its effectiveness and flexibility. The innovative approach sets the stage for creating advanced and productive robotic vision systems in various industries.

Quantitative liquid storage by billiards‐like droplet collision on surfaces with patterned wettability

AbstractThere has been significant interest in researching droplet transport behavior on composite wetting surfaces. However, current research is primarily focused on modifying individual droplets and lacks an in‐depth investigation into high‐precision droplet storage. This study introduces a “billiard ball” droplet transport and storage platform (TSP) with differentiated areas. Within this platform, the volume of droplets stored in the area reaches a consistent threshold through droplet “scrambling,” inspired by the water‐gathering behavior of spiders. The TSP involves connecting two regions of different sizes using a three‐dimensional stepped wedge angle structure. However, this connection is not seamless, leaving a 2‐mm gap between the regions. This gap is intentionally designed to enable continuous droplet transfer while preventing any static migration. Through systematic experimental and simulation analysis, we investigated the influence of superhydrophilic pattern structures and parameters on quantitative droplet storage. We established a functional relationship between the pattern area and the stored volume, and analyzed the intrinsic mechanism of droplet collision separation. This enabled us to achieve on‐demand quantitative droplet storage and autonomize the storage process. The “billiard ball” droplet transport–storage platform proposed in this study holds promising applications in the fields of biomedical and organic chemistry.

Three-stage thermalization of a quasi-integrable system

We consider a system of classical hard rods or billiard balls in one dimension, initially prepared in a Bragg-pulse state at a given temperature and subjected to external periodic fields. We show that at late times the system thermalizes in the thermodynamic limit via a three-stages process characterized by: an early phase where the dynamics is well described by Euler hydrodynamics, a subsequent phase where a (weak) turbulent phase is observed and where hydrodynamic gradient expansion can be broken, and a final one where the gas thermalizes according to viscous hydrodynamics. As the hard rod gas shares the same large-scale hydrodynamics as other quantum and classical integrable systems, we expect these features to universally characterize all many-body integrable systems in generic external potentials. Published by the American Physical Society 2024

Propulsion particle and potential application analysis based on fiber oriented laser propulsion micro-structures

Three kinds of fiber oriented laser propulsion micro-structures (tapered fiber, fiber-capillary, and flat fiber micro-structure) were proposed in this study. The directional of the shock wave generated at the tip of the micro-structure, which can realize the directional propulsion of the particles. The propulsion mechanism, power source, and motion effect of the particles based on the three kinds of propulsion micro-structures were investigated. To better understand the physical mechanism behind the experimental phenomena, physical model of micro-structures were established. The experimental and simulation results demonstrate that the oriented laser propulsion based on three kinds of fiber propulsion micro-structures was dominated by the shock wave ejection mechanism, which was caused by the high pressure of the shock wave. By analyzing the positions of characteristic peaks in the plasma spectra, it is proved that the driving force of particle motion derives from the shock wave formed by the expansion of air plasma. In the process of particle oriented propulsion, it is found that the motion effect of particles strongly depends on the propulsion micro-structure design, laser energy, particle size as well as gap distance d, and it is found that compared with the tapered fiber and flat fiber micro-structure oriented propulsion experiment, the motion effect of particles based on fiber-capillary micro-structure propulsion experiment is more obvious. In addition, based on the characteristic that the fiber oriented laser propulsion micro-structures can realize the directional propulsion of particles, and the micro-structure has shown potential application value in microinjection, laser fun billiard ball, and directional removal of contamination particles inside microsystems, providing theoretical support for later research.

Schumacher against globalism and ecomodernism: Ecology, subsidiarity and the politics of scale

E. F. Schumacher’s Small is Beautiful is one of the most succinct elaborations of Catholic social teaching (CST) and ‘distributism’ – construed as an alternative to both capitalism and socialism. Extending the logic of Polanyi, both market and state, and their right- and left-wing ideological expressions, are shown to be contending forms of collectivism – in that both aggregate the agency of disembedded ‘billiard ball’ individuals. Schumacher’s socio-economic vision is rooted in Livelihood and is orthogonal to both left and right, creating an opportunity for an alternative to modernity involving patterns of embedded production, consumption and reproduction (family, household and place-bound community). ‘Smallness’ and ‘localness’ speak to forms of embedded social capital that are ‘sticky’, viscous and relational, more ascriptive and less fluid. But for precisely this reason, the political agenda implicit in Schumacher’s vision is not only post-liberal, but explicitly both covenantal and Christian. It requires the ontology of sovereign, self-actualizing individuals to be reconnected and constrained through a transcendent relationality with God. Small is Beautiful is shown to be diametrically opposed to the eco-modernist, gnostic and sometimes even transhumanist worldview of global environmentalism.

Best billiard ball in the 19th century: Composite materials made of celluloid and bone as substitutes for ivory.

The demystification of how 19th-century novelly designed materials became significant elements of modern technological, economic, and cultural life requires a complete understanding of the material dimensions of historical artifacts. The objects frequently described as the earliest manufactured plastic products-the billiard balls made by John Wesley Hyatt and his associates from the late 1860s-are examined closely for the first time and are found to be more complex and functionally more successful than has been described. Modern analytical techniques such as optical microscopy, scanning electron microscope-energy dispersive X-ray spectroscopy, X-ray fluorescence, micro-Fourier transformed infrared, and handheld/micro-Raman spectroscopies were used to reveal the complex composition of the Smithsonian Institution's "original" 1868 celluloid billiard ball. Comparisons with billiard and pool balls commercialized from the 1880s to the 1960s showed an unexpected consistency in material formulations. All specimens were made of an unprecedented composite material prepared with a mixture of cellulose nitrate, camphor, and ground bone; the source of the bone was identified as cattle by peptide mass fingerprint (ZooMS). Patent specifications and contemporary journal descriptions explained how and when these formulations emerged. Combining the technical analyses of compositions with a careful reading of the historical record and contemporary descriptions reveals the key elements of the first successful efforts to substitute materials to assist the survival of endangered animals.

Oblique angle collisions between three or more billiard balls

Oblique angle collisions between two balls or two disks have been addressed by many authors. This paper describes oblique angle collisions between three or four billiard balls. Measurements and calculations are presented for cases where one ball is incident obliquely on two or three identical balls, which are in contact and initially at rest. Conservation laws alone are not sufficient to predict the outcome. Adding information about the impact forces on each ball (and ignoring friction forces) provides good theoretical agreement with experimental results.

A note on combined sliding and rolling friction

The coefficient of sliding friction is usually regarded as a constant for any given surfaces although it is sometimes known to vary with sliding speed. An experiment is described where the coefficient of friction for a billiard ball decreases to a very small value as the sliding speed decreases to zero, after which the ball starts rolling without sliding. A simple theoretical explanation is provided.

Solid-body trajectoids shaped to roll along desired pathways.

In everyday life, rolling motion is typically associated with cylindrical (for example, car wheels) or spherical (for example, billiard balls) bodies tracing linear paths. However, mathematicians have, for decades, been interested in more exotically shaped solids such as the famous oloids1, sphericons2, polycons3, platonicons4 and two-circle rollers5 that roll downhill in curvilinear paths (in contrast to cylinders or spheres) yet indefinitely (in contrast to cones, Supplementary Video1). The trajectories traced by such bodies have been studied in detail6-9, and can be useful in the context of efficient mixing10,11 and robotics, for example, in magnetically actuated, millimetre-sized sphericon-shaped robots12,13, or larger sphericon- and oloid-shaped robots translocating by shifting their centre of mass14,15. However, the rolling paths of these shapes are all sinusoid-like and their diversity ends there. Accordingly, we were intrigued whether a more general problem is solvable: given an infinite periodic trajectory, find the shape that would trace this trajectory when rolling down a slope. Here, we develop an algorithm to design such bodies-which we call 'trajectoids'-and then validate these designs experimentally by three-dimensionally printing the computed shapes and tracking their rolling paths, including those that close onto themselves such that the body's centre of mass moves intermittently uphill (Supplementary Video2). Our study is motivated largely by fundamental curiosity, but the existence of trajectoids for most paths has unexpected implications for quantum and classical optics, as the dynamics of qubits, spins and light polarization can be exactly mapped to trajectoids and their paths16.

PSPACE-Completeness of Reversible Deterministic Systems

We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing that any system that can implement three basic gadgets is PSPACE-complete. We then apply this framework to four different systems, showing its versatility. First, we prove that Deterministic Constraint Logic is PSPACE-complete, fixing an error in a previous argument from 2008. Second, we give a new PSPACE-hardness proof for the reversible ‘billiard ball’ model of Fredkin and Toffoli from 40 years ago, newly establishing hardness when only two balls move at once. Third, we prove PSPACE-completeness of zero-player motion planning with any reversible deterministic interacting [Formula: see text]-tunnel gadget and a ‘rotate clockwise’ gadget (a zero-player analog of branching hallways). Fourth, we give simpler proofs that zero-player motion planning is PSPACE-complete with just a single gadget, the 3-spinner. These results should in turn make it even easier to prove PSPACE-hardness of other reversible deterministic systems.

Three Approaches to Platform Studies: Cobweb, Billiard Balls, and Ant Societies

Digital media platforms are becoming increasingly subject to the sway of geopolitics, as seen during the Russian invasion of Ukraine and the US-China trade war. How are platforms becoming geopoliticized? What perspectives shall we use to make sense of the process? This theoretical paper reformulates conceptual apparatuses of liberalism, realism, and constructivism, each represented by a metaphor: the cobweb, billiard balls, and ant societies, respectively. The approaches are introduced, critiqued, and compared to understand platform geopoliticization more historically and imaginatively on global as well as regional and local scales. The discussions propel platform studies to be grounded and multi-layered, concerning not only the apex of politico-economic power but also grassroots and communal praxis, for example, metis. While the pendulum is swinging from transnational capital to nation-states, it is insufficient to restrict our thinking to (neo)realism vis-à-vis (neo)liberalism. A moderate version of constructivism—the “ant societies” model—hence needs articulation, which holds important conceptual and methodological implications.

Independent friction-restitution description of billiard ball collisions

The oblique impact of a cue ball moving on a horizontal surface with an arbitrary spin on an object ball at rest is described using the independent friction-restitution modeling of impact. The model yields theoretical expressions for the post-collision linear and angular velocities in terms of ‘constant’ coefficients of normal restitution, tangential restitution, and friction for both stick and slip regimes of impact. The model also predicts the post-impact velocities reached by the balls when, as a result of friction with the supporting surface, the pure rolling motion is established. Theoretical predictions are in satisfactory agreement with experimental data for collisions between regulation billiard balls, steel, brass, and rubber spheres.

Impact of a cue with a billiard ball

Experimental results are presented to show how the speed and spin of a billiard ball vary as the impact point of the cue is varied above and below the center of the ball. The results are compared with a simple impact model to estimate how the normal and tangential impact forces vary with impact location.

Race, Color, and the Application of Pool Theory

In today’s complex society, we encounter various societal issues. However, race as an attribute and as a major social form tremendously affects many aspects of individuals’ lives, as well as society as a whole. It continues to shape social, political, and economic hierarchies. Many sociological theories that have focused on race and racism, but few have focused on an in-depth understanding of subtle racism and its socio-historical constructs. The purpose of this paper is to discuss and explore race, color, and racism, particularly the subjective form of racism, utilizing the Pool Theory.Pool theory, based on acquired idea from the billiard game, asserts that racism is formed through people’s implicit attitudes, feelings, and behaviors. It emphasizes that race, like many other social concepts, is socially and culturally created by the dominant groups for labeling others to suit their own imagination and goals. Based on generalizations, the theory accentuates that race is subjective and implicit, and that skin color is highly valued in society. According to this theory, those who possess favorite colors are more likely to be seen as superior, influential, valued, and successful in constructing concepts that becomes social reality. The choice of colors and the position of the billiard balls could be the consequence of implicit feelings and biased beliefs about others. Power differentiation, disparity, and colorism are evident in this game. Pool theory refutes color blindness, which is the belief that racism is no longer an issue in American society. The main objective of this study is to encourage future research in theory building, emphasizing the implicit aspects of racism. Additionally, this study can serve as an avenue for literature review, particularly in relation to race and racism.

From Realist Billiard Balls and Liberal Concentric Circles to Global IR’s Venn Diagram? Rethinking International Relations via Turkey’s Centennial

The Republic of Turkey continues to grapple with a foundational tension between isolationist impulses steeped in a nationalist, sovereigntist, i.e., realist outlook on the world, and what I call the “embedded liberalism” of the republican project. Yet, neither realism nor liberalism are sufficient, I show, to explain Turkey’s trajectory. Invoking three visions of the international system as envisaged in realism (billiard balls), liberalism (concentric circles), and global IR (which I conceptualize as a Venn diagram), I argue that the last best captures (Turkey’s) challenges and opportunities. My contention is that global IR incorporates constructivist claims regarding historical and social forces in world politics, but also decenters Eurocentric notions of history and society. A timely way to read multipolarity, the approach supports relational learning regarding our overlapping challenges as humanity. Scholars in and of Turkey arguably have a comparative advantage in this space. This is due to their ability, albeit not always actualized, to read the world in plural terms — the epistemological equivalent of Turkey’s proverbial bridging role in world politics.

Hear π from quantum Galperin billiards

Galperin introduced an interesting method to learn the digits of π by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of π can be observed in the phase shifts of the quantum models.

The Return of Billiard Balls? US–China Tech War and China’s State-Directed Digital Capitalism

Media policy analysts of (neo)liberal persuasion have long seen China as an anomaly. This is, however, a narrow perspective, whose explanatory power pales facing the challenge of recent events. Drawing upon International Relations (IR) theories, this article reflects on the contradicting ideas of (neo)liberalism and (neo)realism in digital media policy, while examining US–China tech war and China’s state-directed platform capitalism. It argues that more attention should be paid to neorealist frameworks, especially Mearsheimer’s offensive realism, which sees the world as consisting of billiard balls bumping into each other, pursuing hegemony. How is offensive realism useful in helping understand recent events about China? How is it also limited? Are we returning to an era of billiard balls? What are the implications for digital media policy to transcend platform capitalism and approach platform socialism?

Newton’s Cradle with Two Balls

When two balls collide multiple times in a simplified Newton’s cradle, the impact point gradually moves away from the lowest point of the swing. The effect was examined using two billiard balls, and was traced to the fact that the upper support points were not separated by exactly one ball diameter.

Natural Selection and Scale Invariance.

This review points out that three of the essential features of natural selection-competition for a finite resource, variation, and transmission of memory-occur in an extremely simple, thermalized molecular population, one of colliding "billiard balls" subject to an anisotropy, a directional flux of energetic molecules. The emergence of scaling behavior, scale invariance, in such systems is considered in the context of the emergence of complexity driven by Gibbs free energy, the origins of life, and known chemistries in planetary and astrophysical conditions. It is suggested that the thermodynamic formalism of statistical multifractality offers a parallel between the microscopic and macroscopic views of non-equilibrium systems and their evolution, different from, empirically determinable, and therefore complementing traditional definitions of entropy and its production in living systems. Further, the approach supports the existence of a bridge between microscopic and macroscopic scales, the missing mesoscopic scale. It is argued that natural selection consequently operates on all scales-whether or not life results will depend on both the initial and the evolving boundary conditions. That life alters the boundary conditions ensures nonlinearity and scale invariance. Evolution by natural selection will have taken place in Earth's fluid envelope; both air and water display scale invariance and are far from chemical equilibrium, a complex condition driven by the Gibbs free energy arising from the entropy difference between the incoming solar beam and the outgoing infrared radiation to the cold sink of space acting on the initial conditions within evolving boundary conditions. Symmetry breaking's role in the atmospheric state is discussed, particularly in regard to aerosol fission in the context of airborne bacteria and viruses in both current and prebiotic times. Over 4.4 billion years, the factors operating to support natural selection will have evolved along with the entire system from relative simplicity to the current complexity.

Complex-chamber hydrogel actuators based on strong interfacial adhesion for fluid-driven multi-degree-of-freedom motions

Hydrogel actuators with fast responsive speed, large driving power, diverse motions, superior mechanical properties and good environmental adaptability could be a suitable candidate for complex-task scenarios. However, a complete aggregation of these above characteristics is rarely reported, due to limitations from processing methods, raw materials and structural configuration of present hydrogel actuators. Herein we designed and fabricated complex-chamber-structure hydrogel actuators basing on soft interfacial adhesion of aluminum hydroxide nanocomposite hydrogels without any mold, template and valuable equipment, demonstrating that this method possessed simple, facile and inexpensive features. These composite hydrogels showed high tensile (0.5–1.0 MPa) and compressive (2–15 MPa) resistance properties, much higher than those of previously reported fluid-driven hydrogel actuators, which meant that our hydrogel actuators could have a higher cargo loading capacity. The cavity-structure soft actuators owned superior sealability and self-recoverability, and could give rapid uniaxial expansion and multidirectional large-scale bending under fluid actuation. Furthermore, those actuators with sucker structure were able to transfer heavy objects (e.g. 80 g glass plate and 180 g billiard ball) from water to air, and also move a plastic plate from back to right in three-dimensional space, indicating that this complex-cavity hydrogel actuators could suit to multi-task scenarios. The exquisitely assembled process of intricate chamber structure will offer a novel approach for hydrogel actuators with diversified driving functions.