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In this paper, we define non-linear versions of Banach–Mazur distance in the contact geometry set-up, called contact Banach–Mazur distances and denoted by $$d_\mathrm{CBM}$$ . Explicitly, we consider the following two set-ups, either on a contact manifold $$W \times S^1$$ where W is a Liouville manifold, or a closed Liouville-fillable contact manifold M. The inputs of $$d_\mathrm{CBM}$$ are different in these two cases. In the former case the inputs are (contact) star-shaped domains of $$W \times S^1$$ which correspond to the homotopy classes of positive contact isotopies, and in the latter case the inputs are contact 1-forms of M inducing the same contact structure. In particular, the contact Banach–Mazur distance $$d_\mathrm{CBM}$$ defined in the former case is motivated by the concept, relative growth rate, which was originally defined and studied by Eliashberg–Polterovich. The main results are the large-scale geometric properties in terms of $$d_\mathrm{CBM}$$ . In addition, we propose a quantitative comparison between elements in a certain subcategory of the derived categories of sheaves of modules (over certain topological spaces). This is based on several important properties of the singular support of sheaves and Guillermou–Kashiwara–Schapira’s sheaf quantization.

The ride quality of the railway vehicle is not only affected by the wheel-rail contact geometry but also by the yaw damper. In order to explore this variation law, an equivalent parameter model of the yaw damper was established based on the internal characteristics of the yaw damper, which is both accurate and efficient. Then, considering the influence of wheel wear and wheel-rail contact geometry, ride quality of the railway vehicle under different parameters of yaw damper and wheel-rail contact parameters was analysed. The results show that the wheel-rail contact points are scattered on the wheel profile after the wheel wears out, and the equivalent conicity also tends to increase with the increasing operating mileage. The distribution of ride quality space is sensitive to the change of equivalent conicity. In the low equivalent conicity area, the expansion rate of excellent ride quality space is faster. In the high equivalent conicity area, the expansion rate of qualified ride quality space is faster. Appropriate additional stiffness which is oil stiffness in parallel with structural damping in the equivalent parameter model of the yaw damper can improve the vehicle ride quality. The lateral ride quality is influenced obviously with the condition of the damping of the yaw damper being less than 440 kN·s·m−1. Properly reducing the joint stiffness of the yaw damper could reduce the influence of characteristic parameters of the yaw damper and equivalent conicity of the wheel-rail contact on vehicle lateral ride quality. The optimized characteristic parameters of the yaw damper are used in the actual vehicle test, and the ride quality is effectively improved.

A general model is developed, and on its basis, there are special models formulated of the grinding process with crossed axes of the tool and workpiece with a profile in the form of a circle arc. A new method of control of the grinding process is proposed, which will provide processing by equidistant curves, and the amount of cutting of a circle equal to the allowance. This will increase the productivity and quality of grinding. The presented method of grinding implements the processing with the spatial contact line of the tool and workpiece. When the axes are crossed, the contact line is stretched, which leads to an increase of the contact area and, accordingly, to a decrease of the temperature in the processing area. This allows processing of workpieces with more productive cutting conditions.

Polyoxometalates (POMs) are promising candidates for molecular electronic applications because (1) they are inorganic molecules, which have better CMOS compatibility compared to organic molecules; (2) they are easily synthesized in a one-pot reaction from metal oxides (MOx) (where the metal M can be, e.g., W, V, or Mo, and x is an integer between 4 and 7); (3) POMs can self-assemble to form various shapes and configurations, and thus the chemical synthesis can be tailored for specific device performance; and (4) they are redox-active with multiple states that have a very low voltage switching between polarized states. However, a deep understanding is required if we are to make commercial molecular devices a reality. Simulation and modeling are the most time efficient and cost-effective methods to evaluate a potential device performance. Here, we use density functional theory in combination with nonequilibrium Green’s function to study the transport properties of [W18O54(SO3)2]4–, a POM cluster, in a variety of molecular junction configurations. Our calculations reveal that the transport profile not only is linked to the electronic structure of the molecule but also is influenced by contact geometry and presence of ions. More specifically, the contact geometry and the number of bonds between the POM and the electrodes determine the current flow. Hence, strong and reproducible contact between the leads and the molecule is mandatory to establish a reliable fabrication process. Moreover, although often ignored, our simulations show that the charge balancing counterions activate the conductance channels intrinsic to the molecule, leading to a dramatic increase in the computed current at low bias. Therefore, the role of these counterions cannot be ignored when molecular based devices are fabricated. In summary, this work shows that the current transport in POM junctions is determined by not only the contact geometry between the molecule and the electrode but also the presence of ions around the molecule. This significantly impacts the transport properties in such nanoscale molecular electronic devices.

Let $f$ be a Morse function on a closed surface $\Sigma$ such that zero is a regular value and such that $f$ admits neither positive minima nor negative maxima. In this expository note, we show that $\Sigma\times \mathbb{R}$ admits an $\mathbb{R}$-invariant contact form $\alpha=fdt+\beta$ whose characteristic foliation along the zero section is (negative) weakly gradient-like with respect to $f$. The proof is self-contained and gives explicit constructions of any $\mathbb{R}$-invariant contact structure in $\Sigma \times \mathbb{R}$, up to isotopy. As an application, we give an alternative geometric proof of the homotopy classification of $\mathbb{R}$-invariant contact structures in terms of their dividing set., Comment: 15 pages, 5 figures. Expository note

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplectic setting. In particular, we construct scattering-symplectic spheres and scattering symplectic gluings between strong convex symplectic fillings of a contact manifold. By giving an explicit computation of the Poisson cohomology of a scattering symplectic manifold, we also introduce a new method of computing Poisson cohomology., Final version accepted for publication in the Pacific Journal of Mathematics (PJM)

The power conserving interconnection of port-thermodynamic systems via their power ports results in another port-thermodynamic system, while the same holds for the rate of entropy increasing interconnection via their entropy flow ports. Control by interconnection of port-thermodynamic systems seeks to control a plant port-thermodynamic system by the interconnection with a controller port-thermodynamic system. The stability of the interconnected port-thermodynamic system is investigated by Lyapunov functions based on generating functions for the submanifold characterizing the state properties as well as additional conserved quantities. Crucial tool is the use of canonical point transformations on the symplectized thermodynamic phase space., 7 pages. arXiv admin note: text overlap with arXiv:2102.05493

The contact geometry of rough surfaces markedly affects the functional properties such as sealing and lubrication. The effect of surface roughness on the percolation characteristic of elastic contact was studied. The elastic contact of randomly rough surfaces with a glass plate was performed using four different surface roughnesses of silicone rubber blocks as specimens. The results illustrate that the percolation threshold was significantly affected by the valley morphology of a surface. The increase in depth and void volume of valleys improved the connectivity between valleys, but impeded the coalescence of contact clusters, resulting in the extinction of the spanning void cluster allowing fluid flow when the relative contact area was large. Furthermore, the critical pressure and connectivity at the percolation threshold were related to the maximum peak height and autocorrelation length of a surface, respectively.

In this paper, we explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer excisions, which was introduced to the context of sutured monopole Floer homology by Kronheimer and Mrowka. We then compute the sutured monopole Floer homology of some special balanced sutured manifolds, using tools closely related to contact geometry. For application, we obtain an exact triangle for the oriented skein relation in monopole theory and derive a connected sum formula for sutured monopole Floer homology., Comment: 34 pages, 11 figures. Correct typos in the new version. Comments are welcomed!

Gears are important motion and power transmission components and enhancing their machining accuracy and performance. In this work, a novel processing of ultrasonic vibration-assisted forming grinding gear (UVAFGG) is proposed, which involves the superimposition of ultrasonic vibration on the gear, and the thermo-mechanical coupling effect on surface residual stress is explored as well. Firstly, based on the local contact geometry relationship for forming grinding, the three-dimensional (3D) distribution model of the heat flux density along the tooth profile is established. In addition, the mathematical relationship models between the grinding force, grinding heat, residual stress, and grinding parameters are also given. Then, the effect of grinding parameters such as spindle speed and ultrasonic amplitude for the characteristics of residual compressive stress accumulation is obtained by comparing the single factor experimental and finite element simulation results. It is found that under the action of ultrasonic vibration, the grinding heat and grinding force reduce by 38.7% and 40.5 % and 40.5 %, respectively. The surface residual compressive stress gradually decreases with the increase in spindle speed, while with the increase in ultrasonic amplitude, it increases first and then decrease. Comparing with the conventional grinding gear (CGG), the average rate of increase of the surface residual compressive stress under the both parameters is 17.8 %–31.3 % and 20 % respectively. Meanwhile, the residual compressive stress along involute shows a negative correlation with the increase in the rolling angle. At the same time, the experimental and simulation results agree well with the theoretical model. In conclusion, the results of this study provide a novel process technology for gear machining, and a reference for the investigation on residual stress during UVAFGG.

A calculation model of grinding temperature during full tooth groove form grinding (FTGFG) was established through the simplification of the three-dimensional (3D) heat conduction process and based on the theoretical analysis of the transient moving heat source temperature field. The proposed model calculated the grinding temperature distribution of the gear surface and also described the coupling effect of two adjacent grinding heat sources at the junction of the tooth groove. Based on the grinding principle and the contact geometry relationship between the formed grinding wheel and the workpiece, the distributions of grinding parameters, grinding wheel geometry parameters, the actual contact arc length between the grinding wheel and the workpiece, tangential grinding force, and the heat partition to the workpiece were analyzed. A 3D non-uniform heat flux distribution model was also developed based on the actual tangential grinding force distribution, the linear velocity distribution of the grinding wheel, the heat partition ratio along the cross-section of the tooth groove, and the triangular heat flux model in the direction of the contact arc for the contact zone during FTGFG. Finally, a test method for form grinding temperature measurement was designed, and the theoretical model was verified by experimental results. Test results revealed that the temperature distribution on the tooth groove surface during form grinding was non-uniform. Due to the coupling effect of two adjacent heat sources, the temperature increased sharply, and a steep peak was formed at the flange where the bottom plane and the transition arc intersected or the transition arc and the involute intersected. A comparison between experimental and theoretical results on the ground surface and in the transverse section revealed that the analytical model had better prediction accuracy and that the relative error was within 15 %.

We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin’s maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely integrable and its quadrature-based solution is given. : contact geometry, thermodynamics, optimal control, Hamiltonian systems, integrability

Traditional physics-based contact models have been widely used for describing various contact phenomena such as robotic grasping and assembly. However, difficulties in carrying out contact parameter identification as well as the relatively low measurement accuracy due to complex contact geometry and surface uncertainties are the limiting factors of the physics-based contact modeling methods. In this paper, we present a novel hybrid contact modeling (HCM) method as an endeavor to discover models that can more accurately simulate practical contact scenarios than traditional physics-based contact models. The proposed method is implemented by combining a physics-based contact model and a data-driven error model. This approach is validated by using simulations of a bouncing ball, a flat-shot, and a three-dimensional (3D) peg-in-hole. The results demonstrate the feasibility and consistent performance of the HCM method.

A model is proposed for calculating the actual radial feed in internal grinding on a CNC machine. The model establishes the relation between the actual and programmed feed, as a function of the cutting forces, the elastic deformation of the machining system, the cutting conditions, the wheel–workpiece contact geometry, the wheel characteristics, and other parameters. The model is used to predict the change in radius of the machined hole surface in the workpiece, from the initial to the final value for a specified automatic cycle, in various internal-grinding conditions. The model provides the basis for multiparametric optimization of the grinding cycles in multidimensional control-parameter space.

A new and simple kind of all-carbon junction nanodevice, which is free of metal electrodes, is constructed by carbon chains seamlessly connected to two graphyne nanoribbons (GYNRs) electrodes. The electron transport properties of the constructed nanodevices are systematically investigated using self-consistent charge density-functional tight-binding combined with nonequilibrium Green’s function (NEGF) formalism. The effects of contact type and contact position on the electron transport properties of these devices are discussed. The calculated results show that the electron transport properties can be well modulated by the contact geometry of the carbon chain. In GYNRs connected by both horizontal and tilted single-carbon chain, an evident even–odd behavior of conductivity is observed. In addition, the linear, monotonous currents in a wide bias voltage range show good Ohmic contact. The negative differential resistance also appears under both positive and reverse bias voltages, indicating applications in bidirectional tunnel diodes. Comprehensive analyses of the physical mechanisms for the odd–even behavior are given. Remarkably, in GYNRs connected by double-carbon chains, a noticeable current stabilizer behavior occurs, suggesting that the graphyne nanodevices contacted with double-carbon chains can be used as a current stabilizer in circuits. This article provides valuable insight into all-carbon functional nanodevices.

Wet adhesion is widely adopted in biological adhesion systems in nature, and it is beneficial to design new materials with desired properties based on the underlying physics of wet adhesion. The aim of this work is to develop a design criterion to regulate the wet adhesion. The effects of different contact shapes (flat and sphere) and morphologies of the substrate (smooth, microstructure and nanostructure) on the adhesion force are investigated. Combining with the theoretical models, the dominated factors in the separation process and isolating the viscous contributions from the capillary interactions are evaluated. The results demonstrate that the adhesion mechanisms depend significantly on the capillary numbers of the interstitial liquid and the contact geometry, and the ratio of capillary force to viscous force is a key to regulate the wet adhesion mechanism. These findings can not only explain some phenomena of wet adhesion to organisms, but also provide some inspirations to design new adhesion technology for robotic fingers that can grasp objects in wet environments.

We propose a system containing a single pyrene molecule sandwiched between two metallic electrodes. The transport properties of the single pyrene molecule with four configurations are investigated using a steady-state theoretical model. We calculate the transmission probability and the electric current for the structure (1, 8), the structure (1, 7), the structure (1, 5) and the structure (1, 4). By applying a gate voltage on the pyrene molecule, we calculate the thermoelectric properties. The thermoelectric and electron transport properties can be controlled by quantum interference, the contact geometry and the gate voltage. The asymmetric behavior and the splitting of resonances in the transmission spectrum occur due to applying a gate voltage on the pyrene molecule. As a result, the structures (1, 5) and (1, 7) have a maximum value of the figure of merit reaching to 0.8 at the Fermi level. According to the results, the structures (1, 5) and (1, 7) can be act as promising thermoelectric applications in molecular electronics.

The orientation of, and contacts between, grains of sand reflect the processes that deposit the sands. Grain orientation and contact geometry also influence mechanical properties. Quantifying and understanding sand microstructure thus provide an opportunity to understand depositional processes better and connect microstructure and macroscopic properties. Using x-ray computed microtomography, we compare the microstructure of naturally-deposited beach sands and laboratory sands created by air pluviation in which samples are formed by raining sand grains into a container. We find that naturally-deposited sands have a narrower distribution of coordination number (i.e., the number of grains in contact) and a broader distribution of grain orientations than pluviated sands. The naturally-deposited sand grains orient inclined to the horizontal, and the pluviated sand grains orient horizontally. We explain the microstructural differences between the two different depositional methods by flowing water at beaches that re-positions and reorients grains initially deposited in unstable grain configurations.

Polyacrylamide (PAAm) hydrogels with brush-covered or crosslinked surfaces were produced and their tribological behavior was studied over a wide range of sliding speeds for two different contact geometries: sphere-on-flat and flat-pin-on-flat. Irrespective of the contact geometry, the brushy hydrogel surfaces displayed up to an order of magnitude lower coefficients of friction mu (COF) compared to the crosslinked surfaces, even achieving superlubricity (mu < 0.01). In general, a hydrogel sphere showed a lower coefficient of friction than a flat hydrogel pin at a similar contact pressure over the entire range of sliding speeds. However, after normalizing the friction force by the contact area, the shear stress of hydrogels with either crosslinked or brushy surfaces was found to be similar for both contact geometries at low speeds, indicating that hydrogel friction is unaffected by the contact geometry at these speeds. At high sliding speeds, the shear stress was found to be lower for a sphere-on-flat configuration compared to a flat-pin-on-flat configuration. This can be attributed to the larger equivalent hydrodynamic thickness due to the convergent inlet zone ahead of the sphere-on-flat contact, which presumably enhances the water supply in the contact, promotes rehydration, and thus reduces the friction at high sliding speeds compared to that measured for the flat-pin-on-flat contact., Friction, 10 (3), ISSN:2223-7704, ISSN:2223-7690

We improve the previous result “A complete Ricci soliton whose metric g is K-contact and the soliton vector field X is strictly contact, is compact Sasakian Einstein” and show that, if a complete Ricci soliton (M, g, X) whose metric g is a contact metric and the soliton vector field X is strictly contact, then X is an infinitesimal automorphism and g is Einstein. Finally, for a Ricci soliton with X as the Reeb vector field, we show that (M, g) is compact Einstein and and Sasakian.

In the present paper, we initiate the study of $$*$$ - $$\eta $$ -Ricci soliton within the framework of Kenmotsu manifolds as a characterization of Einstein metrics. Here we display that a Kenmotsu metric as a $$*$$ - $$\eta $$ -Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have developed the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost $$*$$ - $$\eta $$ -Ricci soliton. Next, we deliberate $$*$$ - $$\eta $$ -Ricci soliton admitting $$(\kappa ,\mu )^\prime $$ -almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to $${\mathbb {H}}^{n+1}(-4)\times {\mathbb {R}}^n$$ . Finally we present some examples to decorate the existence of $$*$$ - $$\eta $$ -Ricci soliton, gradient almost $$*$$ - $$\eta $$ -Ricci soliton on Kenmotsu manifold.

In this paper, we present some initial results aimed at defining a framework for the analysis of thermodynamic systems with additional restrictions imposed on the intensive parameters. Specifically, for the case of chemical reactions, we considered the states of constant affinity that form isoffine submanifolds of the thermodynamic phase space. Wer discuss the problem of extending the previously obtained stability conditions to the considered class of systems.

An active seating system is designed to promote dynamic sitting. To achieve this, the user’s posture is permanently monitored by sensors. If the user does not change posture independently within a defined period of time, actuators exert a strain on the buttocks to create subconscious discomfort. This discomfort is intended to induce the user to change posture without consciously noticing it. In previous studies, measurements were carried out on an automated test bench based on a modified office chair. In this context, the actuating forces and displacement at which the user consciously perceives discomfort were determined, as well as the influence of different actuator speeds. The first measurements were carried out with a flat surfaced actuator of 20 mm diameter. This paper investigates the influence of the contact geometry (shape and size) of active seating systems on the human perception threshold. For this reason, the experiments are repeated with nine geometrically different contact geometries with flat, round, and pointed surfaces of 20, 40, and 60 mm diameter. In order to be able to compare results, all measurements are performed with the same group of participants. In addition, questionnaires are used to record subjective parameters during the test. Based on the results, the paper inquires whether, in addition to the expected influence of the diameter of the actuator, a significant influence of shape and speed can be observed.