The radiation efficiency from simple vibrating planar surfaces is often used as a basis to describe the sound radiation from more complex structures, having important applications in various fields of acoustics. The low-frequency radiation efficiency of a baffled piston can easily be represented by a simple monopole source. Notably, the equivalent source strength is dependent on the piston surface area. However, the unbaffled case presents additional difficulties as the so-called ``edge effects'' significantly alter the piston radiation impedance. Consequently, a low-frequency equivalence between dipoles and an unbaffled pistons is not as straight forward, since not only the piston area but also its shape will have an effect on the radiated sound. In this work, the search for a simple and generic, equivalence between dipoles and unbaffled pistons is pursued. A finite element model is used to calculate the radiation efficiency from unbaffled pistons with the same surface area but different shapes. A broad set of results indicate that the ``edge effects'' can be accurately represented by a simple term dependent on the piston compactness (ratio of area to perimeter). Effectively, pist
When a circular symmetric piston suddenly expands into a still gas, a leading shock wave is generated. This paper investigates an inverse problem of reconstructing the trajectory of the piston from the given leading shock front and the given initial flow conditions. We observe that in piston models, as the initial density goes to zero, the piston approaches the shock front; however, in the region between the piston and the shock front, the strict hyperbolicity of the system degenerates. By applying asymptotic analysis, we provide quantitative characterizations of the distance between the piston and the shock front, and the degeneration of strict hyperbolicity. Consequently, by designing appropriate a priori assumptions to balance the benefits and drawbacks arising as the initial density approaches zero, we employ the method of characteristics to prove the global-in-time existence of the piecewise smooth solution for this inverse problem. In particular, the resulting flow structure exhibits significant velocity variations.
We propose a scheme for piston control in a two-ion quantum device with motion confined to orthogonal axes. In this system, one ion plays the role of a ''classical'' piston driven by the Coulomb interaction with the other ion, whose quantum motion is controlled through modulation of its trapping potential. The stationary state is determined self-consistently, taking quantum effects into account. We identify a narrow quantum regime of the ground state connecting two broad classical regimes. We further design inverse-engineering protocols to control the motion of the ''classical'' ion. The proposed control scheme provides a useful route toward controlled piston dynamics in microscopic quantum devices.
This paper investigates the dynamics of a one-dimensional piston expanding into a static rarefied gas. Using asymptotic analysis in the limit of vanishing initial density, we derive sharp estimates for the piston-shock distance, the separation of characteristic speeds, and the reflection coefficient associated with characteristic waves interacting with the leading shock front. Based on these estimates, we apply the method of characteristics to prove the global-in-time existence of piecewise smooth solutions. The resulting flow structure exhibits significant velocity variations. The analysis reveals a stable mechanism that operates in the vanishing-density limit of the piston model.
In this paper, we solve constructively the piston problem for one-dimensional isentropic Euler equations of modified Chaplygin gas. In solutions, we prove rigorously the global existence and uniqueness of a shock wave separating constant states ahead of the piston when the piston pushed forward into the gas. It is quite different from the results of Chaplygin gas or generalized Chaplygin gas in which a Radon measure solution is constructed to deal with concentration of mass on the piston. When the piston pulled back from the gas, we strictly confirm only the first family rarefaction wave exists in front of the piston and the concentration will never occur. In addition, by studying the limiting behavior, we show that the piston solutions of modified Chaplygin gas equations tend to the piston solutions of generalized or pure Chaplygin gas equations as a single parameter of pressure state function vanishes.
We study the piston problem of the compressible fluid flow with the generalized Chaplygin gas. Depending on the inferential critical value of Mach number, we prove that, there exists an integral weak solution for the proceeding piston problem, consisting of a shock separating constant states ahead of the piston if Mach numbers less than this critical value, while a singular measure solution, with density containing a Dirac measure supported on the piston, shall be proposed to solve the proceeding piston problem if Mach numbers greater than or equal to the critical value. For the receding piston problem, rarefaction wave solution always exists when the piston recedes from the gas with any constant speed. Moreover, the occurrence of vacuum state and the convergence of solutions, as well as degeneration of equations are analyzed in the receding case as Mach number tends to infinity.
We explore the dynamics of a hybrid classical-quantum system consisting of a classical piston and a self-interacting pseudospin 1/2 Bose-Einstein condensate with a time-dependent Rabi coupling. We investigate the mechanical work produced by the piston moving as a result of the quantum pressure of the condensate. The time-dependent Rabi field redistributes the condensate density between the spin components and, as a result, causes a time dependent pressure acting on the piston. Correspondingly, the motion of the piston produces quantum evolution of the condensate mass- and spin density profiles. We show how by optimised design of the time-dependent direction of the Rabi field, one can control position and velocity of the piston.
A single-piston quantum engine based on a harmonic oscillator acting as the working fluid is proposed. Using the fact that the interaction between the piston and the oscillator depends on the extent of the oscillator wavefunction, one can control this interaction by modifying the oscillator temperature. By retracting the piston when the interaction is weak (hot oscillator) and returning it to the original position when the coupling is strong (cold oscillator), useful work can be performed assuming the interaction is attractive. The cycle of the engine is simulated numerically using two different powering protocols: bath and measurement. Using the collision model for the baths, the engine is shown to reach a steady state with positive work output.
We are concerned with the one-dimensional piston problem for the compressible Euler equations of Chaplygin gas. If the piston moves at constant subsonic speed to the uniform gas, there exists an integral weak solution for the piston problem, consisting of a shock separating constant states ahead of the piston. While if the speed of the piston is sonic or supersonic, a singular measure solution, with density containing a Dirac measure supported on the piston, shall be introduced to solve the problem. Integral weak solution exists for the piston receding from the gas with any constant speed, and there is no vacuum. In the extreme case as the Mach number of the piston goes to infinity, the limiting equations and solutions are the same as that for the polytropic gases.
We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston remains at the so called mechanical equilibrium. However, the temperatures and densities of the gases may differ across the piston. In that case some earlier studies by Gruber, Piasecki and others reveal a very slow motion (drift) of the piston in the direction of the hotter gas. At the same time the hotter gas slowly transfers its energy (heat) across the piston to the cooler gas. While the previous studies of this interesting phenomenon were only heuristic or experimental, we provide first rigorous proofs assuming that the velocity distribution of the ideal gas satisfies a certain ``cutoff'' condition.
It is a crucial issue to realize real-time piston correction in the area of sparse aperture imaging. This paper introduces an optical diffractive neural network-based piston sensing method, which can achieve light-speed sensing. By using detectable intensity to represent pistons, the proposed method is capable of converting complex amplitude distribution of the imaging optical field into piston values directly. Differing from the electrical neural network, the way of intensity representation enables the method to obtain the predicted pistons without imaging acquisition and electrical processing process. The simulations demonstrate the feasibility of the method for point source, and high accuracies are achieved for both monochromatic light and broadband light. This method can greatly improve the real-time performance of piston sensing and contribute to the development of the sparse aperture system.
We establish the equivalence of free piston and delta shock, for the one-space-dimensional pressureless compressible Euler equations. The delta shock appearing in the singular Riemann problem is exactly the piston that may move freely forward or backward in a straight tube, driven by the pressureless Euler flows on two sides of it in the tube. This result not only helps to understand the physics of the somewhat mysterious delta shocks, but also provides a way to reduce the fluid-solid interaction problem, which consists of several initial-boundary value problems coupled with moving boundaries, to a simpler Cauchy problem. We show the equivalence from three different perspectives. The first one is from the sticky particles, and derives the ordinary differential equation (ODE) of the trajectory of the piston by a straightforward application of conservation law of momentum, which is physically simple and clear. The second one is to study a coupled initial-boundary value problem of pressureless Euler equations, with the piston as a moving boundary following the Newton's second law. It depends on a concept of Radon measure solutions of initial-boundary value problems of the compressible
We consider Casimir force acting on a three dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy in the interior region and the exterior region separated by the piston. It is shown that the divergent term of the Casimir force acting on the piston due to the interior region cancels with that due to the exterior region, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a -- the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like $1/a^4$ when $a\to 0^+$ and decays exponentially when $a\to \infty$. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive
We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M $ and $\frac{N}M $ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite $(A, N, M)$ will be presented. We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M $ and $\frac{N}M $ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to eq
In this paper, the finite temperature Casimir force acting on a two-dimensional Casimir piston due to electromagnetic field is computed. It was found that if mixed boundary conditions are assumed on the piston and its opposite wall, then the Casimir force always tends to restore the piston towards the equilibrium position, regardless of the boundary conditions assumed on the walls transverse to the piston. In contrary, if pure boundary conditions are assumed on the piston and the opposite wall, then the Casimir force always tend to pull the piston towards the closer wall and away from the equilibrium position. The nature of the force is not affected by temperature. However, in the high temperature regime, the magnitude of the Casimir force grows linearly with respect to temperature. This shows that the Casimir effect has a classical limit as has been observed in other literatures.
We study the Casimir force in piston-like geometries semiclassically. The force on the piston is finite and physical, but to leading semiclassical approximation depends strongly on the shape of the surrounding cavity. Whereas this force is attractive for pistons in a parallelepiped with flat cylinder head, for which the semiclassical approximation by periodic orbits is exact, this approximation to the force on the piston vanishes for a semi-cylindrical head and becomes repulsive for a cylinder of circular cross section with a hemispherical head. In leading semiclassical approximation the sign of the force is related to the generalized Maslov index of short periodic orbits between the piston and its casing.
We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is
We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area $A$ of the cross-section, the mass $M$ of the piston, and the number $N$ of particles go to infinity keeping $A/M$ and $N/M$ fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption.
We study high Mach number limit of the one dimensional piston problem for the full compressible Euler equations of polytropic gas, for both cases that the piston rushes into or recedes from the uniform still gas, at a constant speed. There are two different situations, and one needs to consider measure solutions of the Euler equations to deal with concentration of mass on the piston, or formation of vacuum. We formulate the piston problem in the framework of Radon measure solutions, and show its consistency by proving that the integral weak solutions of the piston problems converge weakly in the sense of measures to (singular) measure solutions of the limiting problems, as the Mach number of the piston increases to infinity.
We consider a massive inelastic piston, whose opposite faces have different coefficients of restitution, moving under the action of an infinitely dilute gas of hard disks maintained at a fixed temperature. The dynamics of the piston is Markovian and obeys a continuous Master Equation: however, the asymmetry of restitution coefficients induces a violation of detailed balance and a net drift of the piston, as in a Brownian ratchet. Numerical investigations of such non-equilibrium stationary state show that the velocity fluctuations of the piston are symmetric around the mean value only in the limit of large piston mass, while they are strongly asymmetric in the opposite limit. Only taking into account such an asymmetry, i.e. including a third parameter in addition to the mean and the variance of the velocity distribution, it is possible to obtain a satisfactory analytical prediction for the ratchet drift velocity.