Double well potentials and quantum gates

Particle systems have many applications, with the most popular being to produce special effects in video games and films. To permit particle systems to be created quickly and easily, Particle System Interfaces (PSIs) have been developed. A PSI is a piece of software designed to perform common tasks related to particle systems for clients, while providing them with a set of parameters whose values can be adjusted to create different particle systems. Most PSIs are inflexible, and when clients require functionality that is not supported by the PSI they are using, they are forced to either find another PSI that meets their requirements or, more commonly, create their own particle system or PSI from scratch. This paper presents three original contributions. First, it identifies 18 features that a PSI should provide in order to be capable of creating diverse effects. If these features are implemented in a PSI, clients will be more likely to be able to accomplish all desired effects related to particle systems with one PSI. Secondly, it introduces a novel use of events to determine, at run time, which particle system code to execute in each frame. Thirdly, it describes a software architecture called the Dynamic Particle System Framework (DPSF). Simulation results show that DPSF possesses all 18 desirable features.

Modeling the C. elegans nematode and its environment using a particle system

Non-linear elasto-plastic shock waves in particle systems at high-velocity compaction are simulated by the discrete element method. The contact laws applied between the spherical metal particles include non-linear elastic and plastic loading, adhesion and elastic unloading. Of particular interest is to study the transmission and reflection of non-linear shock waves through a particle system with and without voids between the particles. Interesting results are presented in the paper including the particle deformation at incident and reflected shocks and particle velocity oscillations as a result of voids. The study of non-linear elasto-plastic shock waves in particle systems has a strong practical relevance including high-velocity compaction of metal powder.

Simulation purposes are to create an event in the world as real as possible, and by using Virtual Reality Technologies, it can achieve a higher level of realism and immersion. By using particle Systems from Unity can be used to producing a phenomenon that involving a small moving object on a big scale such as smoke, fire, or rain. However, when trying to use the particle system, sometimes the performance got reduced because there are too many particles working at the same time and result in a frame rate drop that causing discomfort to the player. For this reason, it's essential to optimize the performance by limiting objects that are needed to draw to lighten up the GPU process. In this paper, we discussed how to produces rain using the particle system in unity and find the best way to simulating rain with the best frame rate. We will show how the lifetime of the particle affecting the cycle of the particle system and the impact on the particle emission. We concluded that it's essential for developers to focus on the balance for creating realistic and detailed simulation and the stability of the simulation performance so the player can be more comfortable and immersive.

Granular particles systems under vertical vibration exhibit Brazilian Nut separation (BN), Reversed BN (RBN) separation or transitional phases at different vibrating conditions. In the present work, we investigate the influence of rotation on the BN separation of a binary granular particle system by changing rotational speed. 13X molecular sieve particles with diameter 6.00 mm and 0.60 mm are used. Vibration frequency f is 30 Hz and dimensionless acceleration Γ is 1.52 or 1.75, in which the particle system mainly exhibits BN separation tendency. Rotational speed ω varies from 0 to 150rpm, while the upper surface of the particle system maintains flat. We took the pictures of the particles distribution and measured the particles mass layer by layer to obtain the 3-D distribution of the particles. The results show that rotation enhances the BN separation tendency at slow rotational speed. The BN separation becomes strongest when ω is approximately 50rpm, then the BN separation tendency reduces as ω continues to increase. A butterfly pattern appears in the middle particles layer under the simultaneous stimulations of vibration and rotation.

In quantum mechanics a particle can behave like a particle or a wave. Thus, systems of particles can be likened to a superposition of waves. Since sound can be described as a superposition of frequencies, it can also be described in terms of a system of particles manifest as waves. This metaphor between ‘particle physics’ and sound synthesis is quantitatively developed here, suggested initially from some similarities between the two domains. It is applied to a few fundamental physical principles to show how these can be sonified. The author discusses the process of using a simulated ‘atom trap’ to compose a piece that does not require a physicist to appreciate it. This metaphor blurs the distinctions between science and art, where scientific experiment becomes musical composition, and exploring a musical idea involves playing with particle system dynamics. In the future, methods like these could be used with a real system of particles – the particle accelerator will become an expressive musical instrument, and the particle physicist will become the composerscientist.

Imagine you could produce an artificial crystal for quantum matter, defect free and with complete control over the periodic crystal potential. The shape of the periodic potential, its depth and the interactions between the underlying particles could be changed at will and the particles could be moved around in a highly controlled way, at essentially zero temperature. This sounds almost too good to be true, but it is in fact what optical lattices have made possible for cold and ultracold atoms.

Fingering instability in particle systems

In 1975, Moser introduced the map σ to linearize the motion of the Calogero—Moser—Sutherland model with rational inverse square potential. This linearizing map was unusual in that it turned out to be an involution on the phase space. In 1990, Wilson introduced an involution on a part of the Sato Grassmannian to demonstrate the bispectrality of certain Kadomtsev—Petviashvili (KP) solutions. Using the correspondence between particle systems and the poles of KP solutions, one may then also view Wilson’s bispectral involution as a map on the phase space of the particle system and compare them. As a result, we find that the bispectral involution is the linearizing map of the Calogero—Moser particle system and that it generates nonisospectral master symmetries of the KP flows. This chapter will review this material and then update it with reference to recent papers of Wilson, Shiota, Kasman—Rothstein, and Rothstein that simplify the proof and extend the results to include other integrable Hamiltonian systems of particle systems with linearizing involutions.

We study the Fleming-Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity.This asymptotics creates a time scale separation which results in the formation of a condensate of all particles, which then evolves according to a continuous-time Markov chain with jump rates depending in a nontrivial way on both the underlying mutation dynamics and the relative speed of growth to infinity of the killing rate between neighbouring sites.We prove the convergence of the particle system and completely describe the dynamics of the condensate in the case where the number of particles is kept fixed, and partially in the case when the number of particles goes to infinity together with (but slower than) the minimal killing rate.

In the previous chapters we discussed the kinematics and kinetics of a single particle, and we were able to extend the discussion to particle systems and obtain significant equations relating to the kinetics of such systems. In this and the following chapters we apply the equations to rigid bodies, since engineering interest centres on particle systems of this particular kind. We first discuss the kinematics of rigid bodies, recalling that a rigid body is, by definition, a particle system for which the configuration of the particles is unchanging.

We study an interacting particle system whose dynamics depends on aninteracting random environment. As the number of particles growslarge, the transition rate of the particles slows down (perhapsbecause they share a common resource of fixed capacity). Thetransition rate of a particle is determined by its state, by theempirical distribution of all the particles and by a rapidly varyingenvironment. The transitions of the environment are determined bythe empirical distribution of the particles. We prove thepropagation of chaos on the path space of the particles andestablish that the limiting trajectory of the empirical measure ofthe states of the particles satisfies a deterministic differentialequation. This deterministic differential equation involves the timeaverages of the environment process.   We apply the results on particle systems to understand the behavior of computer networks where users access a shared resource using a distributed random Medium Access Control (MAC) algorithm. MAC algorithms are used in all Local Area Network (LAN), and have been notoriously difficult to analyze. Our analysis allows us to provide simple and explicit expressions of the network performance under such algorithms.

In the three-dimensional scene simulation, the realistic sense of flame simulation is of great significance to the simulation effect. Particle systems are widely used as effective simulation methods for irregularly blurred objects. This paper combines the particle system with texture mapping and proposes a more efficient method for generating flame particles. When the initial state of the particle is set, this method introduces a random function to construct a normally distributed particle distribution model. Through a reasonable analysis of the force of the particle, the motion state variation equation of the flame particle is given. On this basis, the texture particles of the flame particles are rendered using square texture sheets in different stages. Finally, the simulation of the environmental factors of the locally attenuated wind field and the dynamic vortex force field makes the flame form more flexible. The results of the study show that while meeting real-time performance, it has a more realistic flame effect.

We present a proof showing that the weak error of a system of $n$ interacting stochastic particles approximating the solution of the McKean–Vlasov equation is $\mathcal{O}({n^{-1}})$. Our proof is based on the Kolmogorov backward equation for the particle system and bounds on the derivatives of its solution which we derive more generally using the variations of the stochastic particle system. The convergence rate is verified by numerical experiments which also indicate that the assumptions made here and in the literature can be relaxed.

Now that most of the game play is sorted out, it’s a good time to look into adding some special effects to spice up the user experience. The most obvious thing that is missing is a variety of sound effects that will help your players keep tabs on the state of the marble’s health while keeping their eyes on the marble and other game pieces. The other missing piece of the puzzle is a favorite of video games of all kinds: the particle system. Particle systems, a mainstay of desktop games, cannot be used with abandon for mobile applications, but with careful planning you can budget in a few for special occasions. Let’s begin with audio, as it will add the most bang for the buck.