Computing Gripping Points in 2D Parallel Surfaces Via Polygon Clipping

To generate suitable grasping positions between tessellated handling objects and specific planar grippers, we propose a 2D analytical approach which uses a polygon clipping algorithm to generate detailed information about the intersection between both objects. With the generated knowledge about the intersection we check whether its shape fits to the set criteria of the operator and represents a valid grasping position. Before the polygon clipping algorithm is applied, a preprocessing step is performed, where appropriate surfaces from the handling object and the gripper are extracted. After rotating all surfaces into a common plane, potential clipping positions are detected and the clipping is performed to get an accurate intersection detection. The validation shows comparable running times to a OBBTree algorithm (0.1 ms per grasping position) while increasing the stability of the results from 30 to 100% for the evaluated test objects.

The methods for the formation of optimal acoustic conditions for the transmission of speech content in small rooms

The subject of research in the article is the methodology for the examination of small-volume premises with a predominance of speech content. The aim of the work is to analyze all stages of acoustic expertise for meeting rooms, conference rooms, press centers, to determine the volume and sequence of the stages, taking into account the specific restrictions and conditions that arise in small rooms. All stages of acoustic expertise are considered in the work on examples of real premises of meeting rooms, conference halls, press centers. The sequence of stages of the examination, when it was carried out for premises of small volumes, did not undergo any changes, compared to the sequence that is used for spectator halls. The main distinctive feature of the first stage of acoustic examination in small rooms with a predominance of speech content is the analysis of the structures of the reverberation process in listening places in order to identify the drawbacks of the formation of a diffuse field, instead of checking the geometry of the wall and ceiling panel walls using geometric theory. A feature of the second stage is the development of recommendations for improving the sound-absorbing properties of enclosing surfaces and eliminating the effect of multiple re-reflections of sound energy between parallel surfaces through the use of partial replacement of surface geometry, work with suspended ceiling structures and the use of sound-absorbing curtains (to correct the properties of glass surfaces). The third and fourth stages of the examination remained unchanged.

Polymerization and Structure of Opposing Polymer Brushes Studied by Computer Simulations

A model of the polymerization process during the formation of a pair of polymer brushes was designed and investigated. The obtained system consisted of two impenetrable parallel surfaces with the same number of chains grafted on both surfaces. Coarse-grained chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions were obtained by a ‘grafted from’ procedure. The structure of synthesized macromolecular systems was also studied. Monte Carlo simulations using the dynamic lattice liquid model were employed using dedicated parallel machine ARUZ in a large size and time scale. The parameters of the polymerization process were found to be crucial for the proper structure of the brush. It was found that for high grafting densities, chains were increasingly compressed, and there is surprisingly little interpenetration of chains from opposite surfaces. It was predicted and confirmed that in a polydisperse sample, the longer chains have unique configurations consisting of a stretched stem and a coiled crown.

A new characterization of null scrolls as parallel surfaces

In this paper, we present a theorem which explains the necessary onditions for parallel surfaces of null scrolls to be surfaces again. Then, we give some properties of parallel ruled surfaces such as the frame fields in terms of the original base curve’s frame vectors, the cases of cross products of these frames’ vector fields. Also, we show the parallel ruled surfaces to be developable from a different point of view. Additionally, we obtain a relation between Gauss curvatures and mean curvatures. Finally, we characterize the striction curve of the parallel ruled surface. In the example, we draw a graph for a particular null scroll and its parallel surface.

Analytical Solution of Problems about the Radiative and Radiative–Conductive Stationary Heat Transfer in a Medium with an Arbitrary Dependence of the Scattering and Absorption on Frequency Boundary Conditions

We defined a method for the analytical solution of problems on stationary radiative and radiative–conductive heat transfer in a medium with an arbitrary frequency dependence of absorption and scattering near its boundary. We obtained formulas for the heat conductance of the remote surface and the thickness of the radiative–conductive relaxation of the medium. We determined characteristics of radiant heat transfer from the medium to free space such as the radiation spectrum, the radiation temperature and the medium outer boundary temperature. In addition, we solved the problem on the radiative–conductive heat transfer from one of two parallel surfaces to another with a medium between them.

Air Bearings Theory, Design and Applications

It is hard to imagine any machine that could operate over a prolonged length of time without a lubricant. It is thus fortuitous that air, with its ubiquitous abundance, can function in this capacity. This is not intuitively obvious, particularly when one deals with parallel surfaces in a thrust bearing. Late Professor Fuller —in his book on the theory and practice of lubrication for engineers, also published by Wiley in 1984—shows the picture of a small thrust bearing with three shoes that can support a 4 lb (17.8 N) thrust runner 5 in. (12.7 cm) in diameter. By simply spinning the runner by hand, one can show that bearing can ride on a thin layer of air for a long time. Running this simple experiment in a classroom has become an eye-opening experience for our engineering students.

The Casimir effect in the presence of infrared transparency

We revisit the Casimir effect perceived by two surfaces in the presence of infrared (IR) transparency. To address this problem, we study a model, where such a phenomenon naturally arises: the DGP model with two parallel 3-branes, each endowed with a localized curvature term. In that model, the ultraviolet modes of the 5-dimensional graviton are suppressed on the branes, while the IR modes can penetrate them freely. First, we find that the DGP branes act as “effective” (momentum-dependent) boundary conditions for the gravitational field, so that the (gravitational) Casimir force between them emerges. Second, we discover that the presence of an IR transparency region for the discrete modes modifies the standard Casimir force — as derived for ideal Dirichlet boundary conditions — in two competing ways: i) The exclusion of soft modes from the discrete spectrum leads to an increase of the Casimir force. ii) The non-ideal nature of the boundary conditions gives rise to a “leakage” of hard modes. As a result of i) and ii), the Casimir force becomes weaker. Since the derivation of this result involves only the localized kinetic terms of a quantum field on parallel surfaces (with codimension one), the derived Casimir force is expected to be present in a variety of setups in arbitrary dimensions.

A simulation study of self-assembly of ABC star terpolymers confined between two parallel surfaces

Phase behavior of ABC star terpolymers confined between two identical parallel surfaces is systematically studied with a simulated annealing method. Several phase diagrams are constructed for systems with different bulk...