Elongated Boxes Research Articles

Characteristic of morphological traits and biochemical indicators in Linum pubescens

The article describes the morphological characteristics and biochemical parameters of a very little studied wild species Linum pubescens (downy flax). This representative of the genus Linum naturally grows in the eastern Mediterranean: Palestine, Syria, Lebanon, Israel, Turkey, Iraq, Greece, Cyprus, Albania. There are brief references to it in the description of the flora of these regions. In Israel, on natural populations of L. pubescens, studies of dimorphic heterostyly, anatomical features of the flower, mechanisms of pollination and incompatibility were carried out. However, other signs, including economically valuable ones, are not described in him. We were the first to study the species ex-situ in a field bank. It was found that in the arid conditions of the southeastern Steppe of Ukraine L. pubescens has a one-year development cycle, a height of 30 cm, 1.2 flowering stems, a bright pink flower with a diameter of 25 mm, a small slightly elongated box with a diameter of 2.7 mm, weight 1000 seeds is 0.6 g, and the leaf area is 218.9 mm2. Plants bloom in mid-July- September. Taking into account the rather large size, the bright color of the flower and the flowering period, we believe that the L. pubescens species has prospects of use as an ornamental flowering plant. In the resulting artificial population of L. pubescens, dimorphic heterostyly is clearly traced. Long and short pest morphs are clearly identified. L. pubescens seeds contain 24% protein and 35% oil. The fatty acid composition of the oil belongs to the "linum-type", like most other types of flax. With a low content of saturated acids (palmitic 6.7% and stearic 2.8%) and a significant predominance of unsaturated acids, especially linolenic up to 64%. It was revealed that this species has a dense non-cracking capsule. This trait is unusual for other flax varieties. Most annual and perennial species are characterized by moderate to severe cracking. Cultivated flax has a non-cracking boll, but not a hard one that breaks easily. It was found that less organic matter and more ash elements accumulate in the capsules and seeds of L. pubescens than in other species of the genus Linum. Probably, this feature, together with non-cracking, helps to better preserve fruits in difficult natural conditions and preserves seed germination for a long time. According to A.A. Zhuchenko, plant genetic resources are divided into six groups. At this stage, L. pubescen is classified as a wild weed relative. It was proposed to include L. pubescens in breeding work to create ornamental varieties in order to transfer it to the improved germplasm group in the future.

Experimental and numerical study of free-surface wave resonance in the gap between two elongated parallel boxes with square corners

Experiments with wave groups are carried out to investigate 3D wave resonance in the gap between two fixed parallel elongated boxes with square corners. The gap responses are re-created in a numerical wave tank using computational fluid dynamics (CFD) with reasonable accuracy. Based on the CFD results with high temporal and spatial resolution, the free-surface behaviour, internal flow velocity and vortex structures near the gap are interrogated in detail to gain insights into the behaviour. It is found that the damping which affects the oscillatory motion in the gap appears to be linear (or at least dominated by linear damping) except for the largest excitation, though substantial flow separation is present. A phase-based harmonic separation method is used to extract the harmonics of the wave field, which is found useful in understanding the dynamics of wave-structure interactions for gap resonance problems.

Energy spectrum of two-particle scattering in a periodic box

We aim to compute the discrete energy spectrum for two-body scattering in a three-dimensional box under periodic boundary conditions. The spectrum in the center of mass is obtained by solving the Schödinger equation in a test potential using the Fourier basis. The focus is on how to project the spectrum into the various irreducible representations of the symmetry groups of the box. Four examples are given to show how the infinite-volume spectrum (including both bound and scattering states) is resolved in cubic or elongated boxes, and in systems with integer or half-integer total spin. Such a demonstration is a crucial step in relating the discrete spectrum in the box to the infinite-volume scattering phaseshifts via the Lüscher method.

Elastic scattering phase shift generalizations to two spin-3 2 particles: On the determination of Ω–Ω scattering phase amplitudes in elongated boxes

The relationship between the elastic scattering phase shifts of the [Formula: see text] system and the two-particle energy spectrum in elongated boxes is established in center-of-mass frame under periodic boundary conditions. The formulas are also extended to cubic boxes to confirm the results in elongated boxes. Our analytical results will be helpful to the study of [Formula: see text] interaction on lattice by using Lüscher’s finite volume method.

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes

The relations between the baryon-baryon elastic scattering phase shifts and the two-particle energy spectrum in the elongated box are established. We studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. Moreover, we discussed the sensitivity functions σ(q) that represent the sensitivity of higher scattering phases. Our analytical results will be helpful to extract the baryon-baryon elastic scattering phase shifts in the continuum from lattice QCD data by using elongated boxes.

Scattering phaseshift formulas for mesons and baryons in elongated boxes

We derive Lüscher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.

Scattering phase-shift formulas for mesons and baryons in elongated boxes

We derive L\"{u}scher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.

Diffusion under Confinement: Hydrodynamic Finite-Size Effects in Simulation.

We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use of periodic boundary conditions in the directions along the surfaces results in dramatic finite-size effects, in addition to that of the physically relevant confining length. As in the simulation of bulk fluids, these effects arise from spurious hydrodynamic interactions between periodic images and from the constraint of total momentum conservation. We derive analytical expressions for the correction to the diffusion coefficient in the limits of both elongated and flat systems, which are in excellent agreement with the molecular simulation results except for the narrowest pores, where the discreteness of the fluid particles starts to play a role. The present work implies that the diffusion coefficients for wide nanopores computed using elongated boxes suffer from finite-size artifacts which had not been previously appreciated. In addition, our analytical expression provides the correction to be applied to the simulation results for finite (possibly small) systems. It applies not only to molecular but also to all mesoscopic hydrodynamic simulations, including Lattice-Boltzmann, Multiparticle Collision Dynamics or Dissipative Particle Dynamics, which are often used to investigate confined soft matter involving colloidal particles and polymers.

Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes.

We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with t ln t and t(3/2) components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments.

Shapes of a liquid droplet in a periodic box.

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slablike as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [L. G. MacDowell, P. Virnau, M. Muller, and K. Binder, J. Chem. Phys. 120, 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable.

Investigations on optical transitions in InAs/InP quantum dash structures

In this paper, we report the dependence of the Gaussian nature of absorption spectra of InAs/InP shallow quantum dot or quantum dash systems on the depth of the dash and also on its relative standard deviation. The dash is considered to be an elongated quantum box with a square base having finite potentials at the boundaries. Our observations reveal that the absorption spectra of the quantum dashes are strongly sensitive to the depth and also on the standard deviation of the dash depth. Predicted results help unveil a better physical insight regarding the optical properties of InAs/InP quantum dash structures. The results are in excellent agreement with reported experimental data of photoluminescence and absorption.

Cooperative box-pushing with multiple autonomous robotic fish in underwater environment

This study presents a cooperative underwater box-pushing scenario, in which three autonomous robotic fish that sense, plan and act on its own move an elongated box from some initial location to a goal location. With the onboard monocular camera, the robotic fish can estimate the pose of the object in the swimming tank. Considering the complexity of the underwater environment and the limited capability of a single robotic fish, the authors address the task by decomposing it into three subtasks and assigning them to capable robotic fish. With one robotic fish observing the box at the goal location and two robotic fish pushing the left and right ends of the box, the box can be moved gradually towards the goal location. The subtask consists of a series of behaviours, each designed to fulfil one step of the subtask. The robotic fish coordinate through explicit communications and distribute the subtasks with a market-based dynamic task allocation method. Task reallocation mechanism that permits robotic fish to auction its assigned task to capable ones is used to cope with unexpected changes in the environment and the limited sensing range of the robotic fish. Experiments are conducted to verify the feasibility of the proposed methods.

Generalized Bose–Einstein Condensation

Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the {}"channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the {}"cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature $T_{c}$ and another "one-dimensional" transition at a lower temperature $T_{1}$ into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, $T_{1}$ merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, $T_{1}$ becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.

Generation of Magnetic Field by Combined Action of Turbulence and Shear

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB proportional S(-1/2) and the growth rate is gamma proportional S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.

Quantum dot infrared photodetectors in new material systems

Infrared detectors were implemented on InAs self-assembled quantum dots fabricated using Stranski–Krastanov growth mode on InAlAs matrix, lattice matched to InP (0 0 1) substrates. These dots grow with a shape of small elongated boxes, with their long axis along the [ 1 ̄ 1 0] direction, and with a high concentration of 7×10 10 cm −2 . Photoconductive measurements were performed in all three polarizations. Rich spectra in the range of 50–500 meV, with different polarization selection rules were observed. The bias dependence of peak intensity of the intraband transitions serves as an additional tool to identify their origin. Some of the peaks, which increase linearly with bias, are attributed to bound-to-continuum transitions. Others, which appear only at larger biases, and increase superlinearly, are due to bound-to-bound transitions. The magnitude of detector responsivity at normal-incidence is similar to that obtained for polarization normal to the layers, and is comparable to that achieved in QWIPs. BLIP conditions prevail at 77 K for integral photocurrent response at F#1. The effect of unintentional doping is discussed. It is shown that this doping can be destructive for detector operation unless the density of dots is large.

Analytic derivation of percolation thresholds in anisotropic systems of permeable objects.

We present a systematic derivation of the percolation thresholds in anisotropic systems composed of permeable elongated boxes. The analytic calculation is based on an order-by-order diagrammatic expansion of the pair-connectedness function. A comparison of the results with those of Monte Carlo simulations shows excellent quantitative agreement. We conclude that, of the analytic methods suggested thus far, the present approach is the most suitable one for quantitative derivation of system properties in continuum percolation.