Circular Trap Research Articles

Quantum signatures of the mixed classical phase space for three interacting particles in a circular trap

Quantum signatures of the mixed classical phase space for three interacting particles in a circular trap

A numerical method for solving snapping out Brownian motion in 2D bounded domains

Diffusion in heterogeneous media partitioned by semi-permeable interfaces has a wide range of applications in the physical and life sciences, including gas permeation in soils, diffusion magnetic resonance imaging (dMRI), drug delivery, thermal conduction in composite media, synaptic receptor trafficking, and intercellular gap junctions. At the single particle level, diffusion across a semi-permeable interface can be formulated in terms of so-called snapping out Brownian motion (SNOBM). The latter sews together successive rounds of reflected BM, each of which is restricted to one side of the interface. Each round of reflected BM is killed when the local time at the interface exceeds an independent, exponentially distributed random variable. (The local time specifies the amount of time a reflected Brownian particle spends in a neighborhood of the interface.) The particle then immediately resumes reflected BM on the same side or the other side of the interface according to a stochastic switch, and the process is iterated. In this paper, we develop a Monte Carlo algorithm for simulating a two-dimensional version of SNOBM, which is used to solve a first passage time (FPT) problem for diffusion in a domain with semi-permeable partially absorbing traps. Our method combines a walk-on-spheres (WOS) method with an efficient algorithm for computing the boundary local time that uses a Skorokhod integral representation of the latter. We validate our algorithm by comparing the Monte Carlo estimates of the mean first passage time (MFPT) to the exact solution for a single circular trap, and show that our simulations are consistent with asymptotic results obtained for the 2D narrow capture problem involving multiple small circular targets. We also discuss extensions to higher dimensions.

Polygons of quantized vortices in Bose-Einstein condensates with a circular trap.

We consider a disk-shaped cold atom Bose-Einstein condensate with repulsive atom-atom interactions within a circular trap, described by a two-dimensional time-dependent Gross-Pitaevskii equationwith cubic nonlinearity and a circular box potential. In this setup, we discuss the existence of a type of stationary nonlinear waves with propagation-invariant density profiles, consisting of vortices located at the vertices of a regular polygon with or without an antivortex at its center. These polygons rotate around the center of the system and we provide approximate expressions for their angular velocity. For any size of the trap, we find a unique regular polygon solution that is static and is seemingly stable for long evolutions. It consists of a triangle of vortices with unit charge placed around a singly charged antivortex, with the size of the triangle fixed by the cancellation of competing effects on its rotation. There exist other geometries with discrete rotational symmetry that yield static solutions, even if they turn out to be unstable. By numerically integrating in real time the Gross-Pitaevskii equation, we compute the evolution of the vortex structures and discuss their stability and the fate of the instabilities that can unravel the regular polygon configurations. Such instabilities can be driven by the instability of the vortices themselves, by vortex-antivortex annihilation or by the eventual breaking of the symmetry due to the motion of the vortices.

Quantum scar affecting the motion of three interacting particles in a circular trap

We propose theoretically a quantum scar affecting the motion of three interacting particles in a circular trap. We numerically calculate the quantum eigenstates of the system and show that some of them are scarred by a classically unstable periodic trajectory, in the vicinity of which the classical analog exhibits chaos. The few-body scar we consider is stabilized by quantum mechanics, and we analyze it along the lines of the original quantum scarring mechanism [Phys. Rev. Lett. 53, 1515 (1984)]. In particular, we identify towers of scarred quantum states which we fully explain in terms of the unstable classical trajectory underlying the scar. Our proposal is within experimental reach owing to very recent advances in Rydberg atom trapping.

Trap Parameters Optimization Based on Metal Particle Dynamic Simulation Method

Insulation failure usually occurs in AC gas-insulated transmission (AC GIL) in field operation, in which the primary cause is the charged motion of metal particles in the electric filed. At present, the particle inhibition method applied is to design particle traps on the inner wall of the GIL shell. However, due to the large randomness of the charged motion for metallic particles and the limitations of field test methods, a particle trap has not yet been designed from the perspective of particle trapping effectiveness. In this paper, firstly, referring to the size of a running 252 kV AC GIL, a 1:1 scaled 3-D similarity simulation model is established to obtain the dynamic characteristics of particles with different sizes under the operating voltage level. This model can form symmetry between the real equipment, and its simulated simulation trajectory can achieve symmetry with the actual one. Secondly, an experimental platform that can easily capture the motion of the particles is set up to experimentally verify the symmetry between the field operating equipment and the simulation model. Finally, the particle traps are set on both sides of the concave and convex surface of the basin insulator, and an optimization scheme for the design of the particle trap is proposed from three aspects: the electric field regulation of the trap, the captured probability of particles, and the trap location. The proposed research shows that, with respect to the motion characteristics of the particles, this paper selects circular hole-shaped trap and its thickness, slot spacing, and slot width are 10 mm, 6 mm, and 8 mm, respectively. When the traps are arranged, one at the bottom of the shell at 70 mm and 80 mm from each side of the concave and convex insulator, the capture probability of the traps on both sides can be as high as 78% and 70%, respectively. Therefore, the analysis and optimization method in this paper has important reference value according to similarity concepts for optimizing particle traps in AC GIL at a certain voltage level.

Two-Dimensional Supersolid Formation in Dipolar Condensates.

Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.

Effect of geometry on dielectrophoretic trap stiffness in microparticle trapping.

Dielectrophoresis, an electrokinetic technique, can be used for contactless manipulation of micro- and nano-size particles suspended in a fluid. We present a 3-D microfluidic DEP device with an orthogonal electrode configuration that uses negative dielectrophoresis to trap spherical polystyrene micro-particles. Traps with three different basic geometric shapes, i.e. triangular, square, and circular, and a fixed trap area of around 900 μm2 were investigated to determine the effect of trap shape on dynamics and strength of particle trapping. Effects of trap geometry were quantitatively investigated by means of trap stiffness, with applied electric potentials from 6 VP-P to 10 VP-P at 1MHz. Analyzing the trap stiffness with a trapped 4.42μm spherical particle showed that the triangular trap is the strongest, while the square shape trap is the weakest. The trap stiffness grew more than eight times in triangular traps and six times in both square and circular traps when the potential of the applied electric field was increased from 6 VP-P to 10 VP-P at 1MHz. With the maximum applied potential, i.e. 10 VP-P at 1MHz, the stiffness of the triangular trap was 60% and 26% stronger than the square and circular trap, respectively. A finite element model of the microfluidic DEP device was developed to numerically compute the DEP force for these trap shapes. The findings from the numerical computation demonstrate good agreement with the experimental analysis. The analysis of three different trap shapes provides important insights to predict trapping location, strength of the trapping zone, and optimized geometry for high throughput particle trapping.

Asymptotics of the principal eigenvalue of the Laplacian in 2D periodic domains with small traps

We derive and numerically implement various asymptotic approximations for the lowest or principal eigenvalue of the Laplacian with a periodic arrangement of localised traps of small \[\mathcal{O}(\varepsilon )\] spatial extent that are centred at the lattice points of an arbitrary Bravais lattice in \[{\mathbb{R}^2}\]. The expansion of this principal eigenvalue proceeds in powers of \[\nu \equiv - 1/\log (\varepsilon {d_c})\], where dc is the logarithmic capacitance of the trap set. An explicit three-term approximation for this principal eigenvalue is derived using strong localised perturbation theory, with the coefficients in this series evaluated numerically by using an explicit formula for the source-neutral periodic Green’s function and its regular part. Moreover, a transcendental equation for an improved approximation to the principal eigenvalue, which effectively sums all the logarithmic terms in powers of v, is derived in terms of the regular part of the periodic Helmholtz Green’s function. By using an Ewald summation technique to first obtain a rapidly converging infinite series representation for this regular part, a simple Newton iteration scheme on the transcendental equation is implemented to numerically evaluate the improved ‘log-summed’ approximation to the principal eigenvalue. From a numerical computation of the PDE eigenvalue problem defined on the fundamental Wigner–Seitz (WS) cell for the lattice, it is shown that the three-term asymptotic approximation for the principal eigenvalue agrees well with the numerical result only for a rather small trap radius. In contrast, the log-summed asymptotic result provides a very close approximation to the principal eigenvalue even when the trap radius is only moderately small. For a circular trap, the first few transcendental correction terms that further improves the log-summed approximation for the principal eigenvalue are derived. Finally, it is shown numerically that, amongst all Bravais lattices with a fixed area of the primitive cell, the principal eigenvalue is maximised for a regular hexagonal arrangement of traps.

The Influence of Information Diffusion on Interbank Risk Contagion

In this paper, the stylized features of incomplete and asymmetric information in the interbank market leading to banks’ precautionary behaviors are introduced. Based on banks’ stylized behavioral rules, the influencing mechanism of information diffusion on interbank risk contagion is analyzed, and how the existence of information diffusion and banks’ information-obtaining ability influence the interbank risk contagion is verified through computational simulations. The results show that information diffusion can significantly accelerate the process of and magnify the extent and probability of interbank risk contagion, and improving banks’ information-obtaining ability could lower the speed and extent of the interbank risk contagion. This paper also finds and explains some special phenomena of rollover risk contagion when information diffusion exists: the saltatory risk contagion, the circular liquidity trap, and the risk discovery of information diffusion.

Vortices with massive cores in a binary mixture of Bose-Einstein condensates

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying them their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Abstract The most reliable estimates of the population abundance of ground‐dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical‐based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two‐fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems.

An Efficient Source Location Privacy Protection Algorithm Based on Circular Trap for Wireless Sensor Networks

With the aim of addressing the problem of high overhead and unstable performance of the existing Source Location Privacy (SLP) protection algorithms, this paper proposes an efficient algorithm based on Circular Trap (CT) which integrates the routing layer and MAC layer protocol to provide SLP protection for WSNs. This algorithm allocates time slots for each node in the network by using Time Division Multiple Access (TDMA) technology, so that data loss caused by channel collisions can be avoided. At the same time, a circular trap route is formed to induce an attacker to first detect the packets from the nodes on the circular route, thereby moving away from the real route and protecting the SLP. The experimental results demonstrate that the CT algorithm can prevent the attacker from tracking the source location by 20% to 50% compared to the existing cross-layer SLP-aware algorithm.

Vortex-lattice in a uniform Bose–Einstein condensate in a box trap

We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose–Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman’s universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross–Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state.

Tuning the self-organization of confined active particles by the steepness of the trap.

We consider the collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with small rotational fluctuations. They also interact with each other via soft, isotropic, repulsive potentials. The particles are confined in a circular trap. The steepness of the trap is tuneable. The average packing fraction of the particles is low. When the trap is steep, particles flock along its boundary. They form a polar cluster that spreads over the boundary. The cluster is not spatially ordered. We show that when the steepness is decreased beyond a threshold value, the cluster becomes round and compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order. We investigate the kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the cluster needs to roll around its centre of mass to be spatially ordered. We have studied the stability of the order when the trap is suddenly switched off. We find that for the particles with velocity alignment interaction, the decay of the spatial order is much slower than the particles without the alignment interaction.

Quantifying dispersal of a non-aggressive saprophytic bark beetle.

Long distance dispersal to locate suitable breeding sites is recognized as a key trait influencing the population dynamics and distribution of bark beetles and other saprophytic insects. While dispersal behavior has been studied for a range of aggressive ‘tree killing’ bark beetles, few have considered the dispersal behaviour of non-aggressive saprophytic bark beetles that utilize kairomones (host volatiles). We present the results of a mark-recapture experiment that examined adult dispersal patterns of the saprophytic bark beetle Hylurgus ligniperda. Releases took place in summer and autumn 2014, in a clearcut pine forest in the central North Island, New Zealand. Both flight-experienced and flight-naïve adults were marked and released in the center of a circular trap grid that extended to 960 m with 170 or 200 panel traps baited with a kairomone blend of alpha-pinene and ethanol. Of the 18,464 released H. ligniperda, 9,209 (49.9%) of the beetles flew, and 96 (1.04%) of the beetles that flew were recaptured. Individuals were recaptured at all distances. The recapture of flight-experienced beetles declined with dispersal distance, and a diffusion model showed heterogeneous dispersal tendencies within the population. Our best model estimated that 46% of flight-experienced beetles disperse > 1 km, and 1.6% > 5 km. Conversely, no declining pattern was shown in the recapture of flight-naïve beetles, suggesting that emerging H. ligniperda may require a period of flight to initiate chemotropic orientation behavior and subsequent attraction to traps. We discuss the implications of these findings for the management of phytosanitary risks. For instance, combining landscape knowledge of source populations with dispersal processes facilitates estimation of pest pressure at economically sensitive areas such as harvest and timber storage sites. Quantitative dispersal estimates also inform pest risk assessments by predicting spread rates for H. ligniperda that has proven establishment capabilities in other countries.

English

The aim of this study was to determine trap efficiency on capturing fruit fly Ceratitis capitata. The research was conducted in greenhouse of the Entomology Laboratory of the Department of Plant and Environmental Sciences, Agricultural Sciences Center of the Federal University of Paraiba – CCA/UFPB, Areia – PB. The trap efficiency was evaluated by comparing three types (Delta, Pet and Circular Trap) with standard trap of McPhail type using liquid and semi-solid lures: Bio Anastrepha® 5% and CeraTrap®. Traps were equidistantly arranged in the experimental environment where eight releases of 300 adults of C. capitata, newly emerged, were carried out. The effectiveness of traps was evaluated according to the number of captured flies in the set period. Data were subjected to variance analyses and Tukey test. Standard trap of McPhail type and alternative trap of Pet type were the most efficient on capturing C. capitata in greenhouse environment. The alternative trap of Pet type can replace the standard one on C. capitata trapping. Key words: Fruit production, hydrolyzed proteins, Mediterranean fruit fly.

Phase-tunable Josephson junction and spontaneous mass current in a spin-orbit-coupled Fermi superfluid

Atomtronics has the potential for engineering new types of functional devices, such as Josephson junctions (JJs). Previous studies have mainly focused on JJs whose ground states have 0 or $\pi $ superconducting phase difference across the junctions, while arbitrarily tunable phase JJs may have important applications in superconducting electronics and quantum computation. Here we show that a phase tunable JJ can be implemented in a spin-orbit coupled cold atomic gas with the magnetic tunneling barrier generated by a spin-dependent focused laser beam. We consider the JJ confined in either a linear harmonic trap or a circular ring trap. In the ring trap, the magnetic barrier induces a spontaneous mass current for the ground state of the JJ, demonstrating the magnetoelectric effects of cold atoms.

Trap Detection Based Decoding Algorithm for Tail-biting Convolutional Codes

该文分析了循环维特比算法(CVA)中存在的循环陷阱问题，并证明了传统基于CVA的咬尾卷积码译码算法中存在的不足，提出了一种高效率的咬尾卷积码译码算法。该算法通过检测两次不同迭代中获得的两条最大似然路径是否相同来判断是否有循环陷阱产生，并及时终止循环，减少冗余迭代；在没有循环陷阱产生的情况下，新算法比较当前迭代中最大似然路径和已经发现的最优咬尾路径是否相同来自适应终止迭代。文中对循环陷阱检测方案和自适应终止方案做了进一步优化，即利用路径的净增量而非路径本身作为检测量。实验结果表明新算法提高了译码效率，降低了译码复杂度。

On random search: Collection kinetics of Paramecia into a trap embedded in a closed domain

We study the kinetics of a large number of organisms initially spread uniformly in a circular two-dimensional medium, at the center of which a smaller circular trap has been introduced. We take advantage of the acidophily of Paramecium caudatum, which, coming from a neutral medium, penetrates a region of moderate acidity but moves back in the opposite situation when it meets a sharp negative acidity gradient to quantify its rate of irreversible aggregation into a spot of acidified medium in water. Two regimes are distinguished: A ballistic regime characteristic of “fresh” paramecia where the organisms swim in a straight path with a well defined velocity and a Brownian regime characteristic of older paramecia where the mean free path of the organisms is smaller than the system size. Both regimes are characterized by distinct aggregation laws. They both result from a pure random trapping process that appears to have no adaptive strategy.

Plasma potential distribution in tandem surface-plasma source of negative ions

We have experimentally studied the potential distribution in hydrogen plasma and measured its density and electron temperature in the tandem involving a circular multicusp magnetic trap and a positive-to-negative ion convertor. It is confirmed that the plasma potential in the circular trap is lower than the chamber wall potential. It is established that plasma potential in the ion convertor is virtually independent of the convertor potential in the working range.