Frequencies analysis in an infinite beams array

This model consists of a periodic structure formed by solid beams equidistant from each other submerged in a fluid. The beams are clamped at both ends. The distance between the beams, the elastic properties of the solid and the fluid; and the geometric parameters of the beams determine a relationship between the frequencies of the mechanical waves that can propagate through the structure and the wave vector. Analysis within the first Brillouin zone with the Bloch periodicity condition gives rise to frequency bands in which there is the propagation of mechanical waves and bands in which no waves are propagated. Some propagation bands and forbidden regions were found in the examined frequency ranges for various geometric configurations.

Usability of Haptic Volumetric Assistance for Surgical Navigation Tasks

Manual control of surgical instruments represents a sensorimotor control task with at least 3-6 degrees of freedom (DoF). The impact of haptic guidance on volumetric navigation tasks, such as milling of planned volumes for prosthesis fits or preserving sensitive tissues, is investigated. Interaction centered studies are performed to evaluate the usability of the assistance modes for navigation within a volume, along the surface of a volume and around forbidden regions. Results show that haptic assistance can reduce the number of constraint violations, if the virtual stiffness is high enough. However, haptic assistance also can increase error rates when counterforces are close to the absolute perception threshold, as a false sense of security can arise. For navigation along complex surfaces bilateral haptic constraints should be preferred, while unilateral constraints are sufficient for simple geometries. This study complements previous publications as a basis for a flexible rule-based selection or adaptation of modular haptic assistance systems.

Calculation and interpretation of classical turning surfaces in solids

Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs). They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. They can also appear at a monovacancy in a metal. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. Nonetheless, a strong correlation with insulating behavior can still be inferred. Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.

Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

We perform Hamiltonian reduction of a model in which 2 + 1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of ADS2—both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of ADS2 momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

Path planning for automated guided vehicle systems with time constraints using timed Petri nets

Automated guided vehicles (AGVs) are extensively used in many applications such as intelligent transportation, logistics, and industrial factories. In this paper, we address the path planning problem for an AGV system (i.e. a team of identical AGVs) with logic and time constraints using Petri nets. We propose a method to model an AGV system and its static environment by timed Petri nets. Combining the structural characteristics of Petri nets and integer linear programming technique, a path planning method is developed to ensure that all task regions are visited by AGVs in time and forbidden regions are always avoided. Finally, simulation studies are presented to show the effectiveness of the proposed path planning methodology.

Work Statistics and Energy Transitions in Driven Quantum Systems

Thermodynamic quantities of small systems fluctuate and have to be characterised by their appropriate probability distributions. Within the two-point energy measurement prescription, the distribution of work in a quantum system can be derived from the transition probability from initial to final energy. We consider a simple yet representative model system starting in thermodynamic equilibrium and driven by an external force, and compare two different numerical techniques to determine this transition probability with respect to accuracy and numerical effort. In addition, we perform a semi-classical analysis of the process using the WKB approximation. The results agree well with the numerically exact values if Airy-tails modelling the tunnelling into classically forbidden regions of phase space are properly taken into account.

BaTiO3 based photonic time crystal and momentum stop band

Temporally periodic photonic crystals develop an ω-k dispersion relation with momentum band gaps. While conventional photonic crystals induce forbidden bands in the frequency spectrum of photons, photonic time crystals create forbidden regions in the momentum spectrum of photons. This effect allows for enhanced control over many optical processes that require both photonic energy and momentum conservations such as nonlinear harmonic generation. The simulation results show that more intensive scatter fields can obtained in photonic space time crystal. Also, we investigate topological phase transitions of photonic time crystals systems.