Contact Geometry Research Articles

Khovanov homology detects the trefoils

We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact invariants we defined in the instanton Floer setting; a bypass exact triangle in sutured instanton homology, proven here; and Kronheimer and Mrowka's spectral sequence relating Khovanov homology with singular instanton knot homology. As a byproduct, we also strengthen a result of Kronheimer and Mrowka on $SU(2)$ representations of the knot group.

Edge spin transport in the disordered two-dimensional topological insulator WTe2

The spin conductance of two-dimensional topological insulators (2D TIs) is not expected to be quantized in the presence of perturbations that break the spin-rotational symmetry. However, the deviation from the pristine-limit quantization has yet to be studied in detail. In this paper, we define the spin current operator for the helical edge modes of a 2D TI and introduce a four-terminal setup to measure spin conductances. Using the developed formalism, we consider the effects of disorder terms that break spin-rotational symmetry or give rise to edge-to-edge coupling. We identify a key role played by spin torque in an out-of-equilibrium edge. We then utilize a tight-binding model of topological monolayer ${\mathrm{WTe}}_{2}$ and scattering matrix formalism to numerically study spin transport in a four-terminal 2D TI device. In particular, we calculate the spin conductances and characteristic spin decay length in the presence of magnetic disorder. In addition, we study the effects of interedge scattering in a quantum point contact geometry. We find that the spin Hall conductance is surprisingly robust to spin symmetry-breaking perturbations, as long as time-reversal symmetry is preserved and interedge scattering is weak.

Influence of contact geometry over the filament bond of polylactic acid blends

Fused Filament Fabrication is one of the most common Additive Manufacturing technologies among industrial and domestic users because of the satisfying quality of parts and the great variety of thermoplastic polymers available on the market. New possibilities were provided along with the equipment with multiple extrusion systems, referring to multi-colour and multi-material components. Besides part orientation during the manufacturing process, filament bond influences the mechanical properties of parts produced through Fused Filament Fabrication technology. This paper aims to investigate if the bond performance for polylactic acid-based polymers can be enhanced by designing new contact geometries, different from the current surface-to-surface approach. To comprehensively understand the influence of the designed bonding geometries over the tensile strength, all specimens were produced according to a factorial design of experiment method and contact geometries constrained with function related to the nozzle size.

Micro-structuration effects on local magneto-transport in [Co/Pd]IrMn thin films

We measured the local magneto-transport (MT) signal with an out-of-plane magnetic field, including magneto-resistance (MR) and Extraordinary Hall effect (EHE), in exchange-biased [Co/Pd]IrMn thin multilayers that are micro-structured with a 100 μm window. We found that when measured locally around the window, the MT signal deviate from the expected behavior. We studied possible causes, including film micro-structuration, electrical contact geometry as well as magnetic field angular tilt. We found that tilting the magnetic field direction with respect to the normal direction does not significantly affect the MT signal, whereas the positioning and geometry of the contacts seem to highly affect the MT signal. For comparison purposes, we carried these MT measurements using the Van-der-Pauw method on a set of four microscopic contacts directly surrounding the window, and on another set of micro-contacts located outside the window, as well as a set of four contacts positioned several millimeters away of each other at the corners of the wafer. If the contacts are sufficiently far apart, the EHE and MR signals have the expected shape and are not significantly affected by the presence of the window. If, on the other hand, the contacts are micro-positioned, the shape of the EHE signal is drastically deformed, and may be modeled as a mix of the standard EHE and MR signals measured on the outer contacts. Furthermore, if the micro-contacts are located directly around the window, the deformation is amplified, and the weight of the MR signal in the mix is further increased by about 40 %. This suggests that the electron path in the Hall geometry is disturbed by both the proximity of the electrodes and by the presence of the window, which both contribute to the deformation for about two-third and one third, respectively.

Modeling study of milling force considering tool runout at different types of radial cutting depth

Accurate force model during batch precision machining is the basis for optimizing milling parameters and maintaining process stability. Tool radial runout is inevitable and affects milling force, and milling parameters are also important factors affecting milling force. However, existing milling force models rarely consider the influence of tool runout under different types of radial cutting depth, resulting in unsatisfactory accuracy and limited practical application of the models. In this study, a model of the instantaneous undeformed chip thickness of tool considering the effect of tool radial runout is established in stages on the basis of the contact geometry of tool and workpiece. A prediction model for milling force at three types of radial cutting depth is obtained by combining the instantaneous stiffness model. In the model, the true tool radial runout value is calibrated by calculating milling force. The accuracy of the proposed model and the effects of milling parameters on milling force and true tool radial runout are investigated via milling experiments for three types of radial cutting depth. The experimental results show that the proposed milling force model has better accuracy than the models without considering tool runout and considering only tool static runout by comparing milling force curves, the values of R2, and the spectral characteristics of the three models. Milling parameters change the true tool radial runout. The results of this study can provide theoretical guidance for the selection of end milling parameters and theoretical support for maintaining the stability of milling forces in cutting operation.

Modeling of contact interfaces by penalty based enriched finite element method

The present study investigates the frictional contact behavior in engineering materials containing different types of discontinuities or features in the domain by employing the extended finite element method (XFEM). This method is a strong and efficient numerical tool for modeling different types of discontinuities occurring in the domain. The technique models the contact interfaces and other material irregularities independent of the grid or mesh due to which the problems of conformal meshing, remeshing and mesh adaption do not arise. The interface between two contacting bodies is identified by employing the level set method. The Heaviside jump function and level set method are employed to develop local enrichment for contact surfaces. Non-penetration conditions and contact constraints are imposed using the penalty based approach. Split elements are partitioned with triangular sub-elements having higher order Gauss quadrature for the integration over the domain. Finally, several numerical problems are presented to demonstrate the accuracy, efficiency and potential of XFEM in modeling frictional contact between solid bodies with different geometries of contact interfaces. The current work employs XFEM to model circular, elliptical, rectangular and hexagonal contact interface between two solid bodies.

Quantized Nonlinear Conductance in Ballistic Metals.

We introduce a nonlinear frequency-dependent D+1 terminal conductance that characterizes a D-dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a 2D ballistic conductor, we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and Fermi liquid interactions, and we propose experiments on 2D Dirac materials, such as graphene, using a triple point contact geometry.

Friction Issues over the Railway Wheels-Axis Assembly Motion

The frictional issues during motion of the axis-wheels assembly occurring in contact wheel–rail and in bogie bearing were studied. The influence of greases upon friction therein was also considered. The lateral dynamic behavior of the four-axle freight wagon model with two-axle Y25 bogies equipped with swing bolster was analyzed. Simulation models of such a wagon with bogies with and without swing bolsters were elaborated for calculations considering the nonlinearities of wheel–rail contact geometry and nonlinear methods of bogie stability. In these two options, the cases of empty and fully loaded wagon bodies were considered. The lateral dynamic models with 22 and 24 degrees of freedom were considered to determine the nonlinear critical speeds of a freight wagon. It was found that the resistive torque in bearings of the assembly studied varied nonlinearly with wagon speed. During motion along the curve track, values of such a torque can be higher by 50% in case of the wheel under overloading and lower by 50% in case of the wheel under underloading, respectively, compared to those obtained during motion along straight track.

Compression of a pressurized spherical shell by a spherical or flat probe.

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere or compression between two plates. Different theoretical approaches have been developed to retrieve material parameters (e.g.,elastic modulus) or state variables (e.g.,pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

Fractal geometry of contacting patches in rough elastic contacts

Many naturally formed and processed surfaces are rough over a broad range of length scales. Surface roughness reduces the area of contact between solids, with ramifications for phenomena that depend on the geometry of the interface and the amount of direct contact, including friction and adhesion. In this work, we employ large-scale boundary-element simulations for nonadhesive, elastic solids to study the size dependence of contact patch mean pressure and geometry for patches formed between solids with self-affine fractal surface roughness across seven decades in patch area. Contact patches with diameters smaller than a crossover length scale of order the minimum wavelength of roughness are generally compact with simple geometries and bear pressures well described by Hertz theory. The patch pressure in contact patches larger than the crossover scale rises logarithmically before saturating at a finite value. Furthermore, the largest contact patches formed during our simulations are ramified and populated with regions out of contact, or bubbles, which reduce patch area and increase patch perimeter. As a result, we show that the mean contact diameter of the largest patches saturates, indicating that the patch contact area is proportional to the total patch perimeter. We quantify the effects of bubbles on patch area and perimeters as a function of Hurst exponent and contrast our findings with results of comparable bearing-area model calculations. The slow evolution of the mean patch pressure with patch size in our large-scale calculations explains the common observation that the global mean contact pressure depends on the structure of the roughness, the contact area, and even on system size.

Force control of a space robot in on-orbit servicing operations

Force control provided by a small-scaled free-flying space robot on a floating or spinning target will be required for future on-orbit servicing missions, such as detumbling a target, performing an assembly or a maintenance operation. Regarding to different contact geometries for a space robot interacting with a spinning target, this paper addresses the contact model considering its multi-dimensional characteristics. A hybrid motion and force controller is developed to acquire desired contact forces and space robot configuration despite the floating feature of the system. On this basis, the control strategy to implement the operations of three typical phases, namely approaching phase, contact phase and post-contact phase, is proposed. The simulations have been performed to verify the control approaches and visualize the contact scenarios.

Simulation of double-leg stance in conditions of limited hip mobility

Hip osteoarthritis is one of the most common and disabling conditions affecting the elderly. Coxarthrosis is accompanied by impairment of the amortization properties of cartilage, its thinning and destruction, the appearance of pain syndrome, impaired motor functions due to a decrease in muscle strength and the development of stable flexion-adduction contractures, which change congenital motor programs, and, with a prolonged course of degenerative disease, lead to the formation of pathological habits. Objective: to determine the required strength of the muscles of the lower limb in conditions of limited hip mobility to support an upright posture in double-leg stance. Materials and methods. The work of the muscles of the lower extremities under conditions of restricted hip mobility was simulated using the OpenSim 4.0 software. It is based on the ToyLandingModel, which has contact geometry objects to fix the model on the support area. Four models were created: norm (without limitation of joint mobility), model 2 — adduction of 5°, model 3 — adduction of 7°, flexion of 10°, model 4 — adduction of 10°, flexion of 20°, shortening of the femur bones by 2 cm. Results. It was found that with insignificant adduction contractures of the hip joint, the work of the muscles of the lower limb changes slightly during double-leg stance. With flexion-adduction contractures, changes are observed in almost all muscles of the lower limb. There are some peculiarities in the work of muscles under contractures. All the muscles around the thigh reduce the strength necessary to maintain balance, while the lower leg muscles, on the contrary, increase the required strength several times. For example, m.medial gastrocnemius with flexion-adduction contracture and limb shortening develops10 times higher compensatory force (200 N) than in normal conditions (20 N), and although muscle resources are 1500 N, it is very demanding to maintain an upright posture. Similarly, m.tibialis posterior require an increase in strength (threefold), but the antagonist muscle m.tibialis anterior, on the contrary, reduces the force of contraction by an average of 100 N. Conclusions. According to the data of the conducted modeling of double-leg stance with limited hip mobility, it was proved that an increase in limited movements changes the nature of muscle contraction of the entire lower limb and pelvis. The analysis of the obtained results showed that restriction of movements reduces the required force of muscle stabilization around the hip joint, and increases the required force of contraction of the leg muscles. That is, there is an imbalance in the muscles.

Self-Supervised Contact Geometry Learning by GelStereo Visuotactile Sensing

Vision-based tactile sensors have recently shown promising contact information sensing capabilities in various fields, especially for dexterous robotic manipulation. However, dense contact geometry measurement is still a challenging problem. In this article, we update the design of our previous GelStereo tactile sensor and present a self-supervised contact geometry learning pipeline. Specifically, a self-supervised stereo-based depth estimation neural network (GS-DepthNet) is proposed to achieve real-time disparity estimation, and two specifically designed loss functions are proposed to accelerate the convergence of the network during the training process and improve the inference accuracy. Furthermore, extensive qualitative and quantitative experiments of perceived contact shape were performed on our GelStereo sensor. The experimental results verify the accuracy and robustness of the proposed contact geometry sensing pipeline. This updated GelStereo tactile sensor with dense contact geometric sensing capability has predictable application potential in the field of industrial and service robots.

Geometry of contact skew CR-warped product submanifolds of Sasakian manifolds

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products. We establish a lower bound relationship between the squared norm of the second fundamental form and the warping function. The equality case of the inequality is investigated and some special cases of derived inequality are given. Furthermore, we provide non-trivial examples of such submanifolds.

Lifting the non-isothermal CSTR dynamics to the complete Thermodynamic Phase Space

This paper deals with the contact formulation of the contact geometry of irreversible thermodynamics. Firstly, a family of parameterized contact Hamiltonian functions, defined on the complete Thermodynamic Phase Space, generating non-strict contact vector fields which are equivalent on the associated Legendre submanifold, is proposed using both the Gibbs relation and the Gibbs-Duhem relation. Secondly, the parameterized lifts of the CSTR dynamics to the complete Thermodynamic Phase Space are performed, while guaranteeing the global attractivity of the Legendre submanifold on which the dynamics of the system is living.

TRIBOLOGICAL BEHAVIOR OF ALUMINUM COMPOSITES USING TAGUCHI DESIGN AND ANN

In this paper is presented the tribological behavior of A356-based aluminum composites using Taguchi design. Testing of tribological characteristics of aluminum composites was done on a tribometer with block on disc contact geometry. Composite materials were obtained by compocasting. The orthogonal matrix L18 is used to form the experimental design using the Taguchi method. The tribological characteristics of the aluminum composite reinforced with SiC (A356/10 wt.% SiC) were compared to the base material A356 for three sliding speeds (0.25 m/s; 0.5 m/s and 1.0 m/s), three values of normal load (10 N, 20 N and 30 N) and sliding distance of 150 m under lubrication conditions. ANOVA analysis showed that the least wear has a composite material at a load of 10 N and at sliding speed of 0.25 m/s.

Generalized m-quasi-Einstein metric on certain almost contact manifolds

In this paper, we study the generalized m-quasi-Einstein metric in the context of contact geometry. First, we prove if an H-contact manifold admits a generalized m-quasi-Einstein metric with non-zero potential vector field V collinear with ?, then M is K-contact and ?-Einstein. Moreover, it is also true when H-contactness is replaced by completeness under certain conditions. Next, we prove that if a complete K-contact manifold admits a closed generalized m-quasi-Einstein metric whose potential vector field is contact thenMis compact, Einstein and Sasakian. Finally, we obtain some results on a 3-dimensional normal almost contact manifold admitting generalized m-quasi-Einstein metric.

Ultrahigh Anisotropic Transport Properties of Black Phosphorus Field Effect Transistors Realized by Edge Contact

AbstractHighly anisotropic black phosphorus (BP) has recently attracted significant interest for electronic and optoelectronic devices. To date, in‐plane anisotropic properties of BP field effect transistors (FETs) have been reported only with top contact. However, the 2D top contact geometry is unable to measure the in‐plane electrical conductance precisely, due to the presence of the out‐of‐plane conductance, resulting in underestimation of anisotropy. Here, 1D edge contact method is employed to measure the in‐plane conductance precisely along the armchair and zigzag directions of BP without the contribution of out‐of‐plane conductance. The conductance and mobility anisotropies for BP FETs are measured with edge contact at 300 K to be ≈5.5 and ≈7.5, respectively. The results further show that the mobility of BP FETs with edge contact weakly depends on temperature, indicating that the edge roughness scattering limits the mobility. In contrast, the mobility of BP FETs with top contact strongly depends on temperature, showing that the impurity scattering and phonon scattering limit the mobility at below and above 150 K, respectively. Finally, a scattering phase diagram is demonstrated to understand the role of different scattering mechanisms on the modulation of mobility anisotropy in BP FETs with edge and top contacts.

Skinner–Rusk formalism for k-contact systems

In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian systems, which is based on the k-symplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner–Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the second-order condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher's equations, and Maxwell's equations with dissipation terms.

Optimization of the profile and material of wire contacts for an IR photodetector

The study is devoted to the influence of the choice of geometry and materials of wire contacts on the reflection coefficient and thermal characteristics of the photodetector and the quality of the device design. The process of diffusion of materials of wire contacts and contact pads on a photodetector crystal is investigated. The studies were carried out on samples that are rather small in size (250x250x400 um). During the experiment, 4 main types of loop geometry were selected (main loop, reverse loop, double reverse loop, long loop). The loops were formed using a gold wire 25 μm in diameter. The quality of microwelds was investigated in 3 ways: shear and pull-off tests, optical observation using a scanning electron microscope (SEM), and contact resistance measurement. The aim of the work is to create a high-quality design of an IR photodetector, which allows achieving a high sensitivity (at least 0.5 A / W), a large dynamic range (at least 40 dB) and low indicators of dark current values. The developed technology ensures high quality of the photodetector design. Due to the low costs of this technological process (wire material, the number of operations required for installation), relative to other technologies, which allows maintaining high performance in the technical component of the photodetector, the installation method may be of practical interest in production.