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In 1972, Kenmotsu [A class of almost contact Riemannian manifolds, Tohoku Math. J. (2) 24 (1972) 93–103] defined the notion of Kenmotsu manifolds. He has also studied the properties of proper η-Einstein Kenmotsu manifolds, and proved some basic interesting results. These results have been used by a plenty of authors in establishing their main results on Kenmotsu manifolds. Naturally, the question of existence of proper η-Einstein Kenmotsu manifold is a prime question in the study of contact geometry. The main goal of this paper is to discuss the existence of proper η-Einstein Kenmotsu manifolds and to refine some of Kenmotsu’s results. The results of this paper may be used as an erratum of many published papers on Kenmotsu manifolds. In this sequence, we also address the existence of conharmonically flat Kenmotsu manifolds, conformal Ricci flow and almost Ricci solitons on Kenmotsu manifolds. [ABSTRACT FROM AUTHOR]

The ν = 2 / 3 filling is the simplest paradigmatic example of a fractional quantum Hall state, which contains counter-propagating edge modes. These modes can be either in the unequilibrated regime or equilibrated to different extents, on top of a possible edge reconstruction. In the unequilibrated regime, two distinct renormalization group fixed points have been previously proposed, namely Kane–Fischer–Polchinski and Wang–Meir–Gefen. In the equilibration regime, different degree of thermal equilibration may occur, while charge is fully equilibrated. Here, we show that this rich variety of models can give rise to three possible conductance plateaus at e 2 / 2 h (recently observed in experiments), 5 e 2 / 9 h (predicted here), and e 2 / 3 h (observed earlier in experiments) in a quantum point contact geometry. We identify different mechanisms for electrical shot noise generation at these plateaus, which provides an experimentally accessible venue for distinguishing among the distinct models. [ABSTRACT FROM AUTHOR]

Various test structures can be used to determine the specific contact resistivity of ohmic contacts. The transmission line model test structure and circular transmission line model test structure are the most commonly used. The analytical expressions of the former are straightforward and effectively describe the electrical behaviour of a contact, while the concentric geometry of the latter eliminates complications during fabrication. In this article, we present a hybrid test structure that combines the advantages of the transmission line and the circular transmission line models. The analytical expressions of the new structure are presented, and its finite‐element modelling is undertaken. The effect of contact geometry on this test structure is also discussed. Using the presented test structure, determining contact parameters does not require any error corrections. [ABSTRACT FROM AUTHOR]

This study investigates the emission and spectral characteristics of photoconductive THz switches employing coplanar stripline contact geometries fabricated on a GaAs substrate. The experimental results reveal how the power outputs as well as the spectral shape are significantly influenced by the strip width dimension. Utilizing the Drude-Lorentz conductivity model, photocarrier dynamics were analyzed through an RLC circuit framework, offering insights into how the contact design influences the spectral response. Our findings suggest that matching the photocurrent impedance to that of the metallic contacts is critical to improving the efficiency of these devices. [ABSTRACT FROM AUTHOR]

We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature. It can thus be applied to any surface in a region not containing characteristic points. We provide a geometrical interpretation of the coefficients appearing in the expansion, and compute them on some relevant examples in three-dimensional sub-Riemannian model spaces. These results generalize those obtained in [Z. M. Balogh, F. Ferrari, B. Franchi, E. Vecchi and K. Wildrick, Steiner's formula in the Heisenberg group, Nonlinear Anal. 126 (2015) 201–217; M. Ritoré, Tubular neighborhoods in the sub-Riemannian Heisenberg groups, Adv. Calc. Var. 14(1) (2021) 1–36] for the Heisenberg group. [ABSTRACT FROM AUTHOR]

We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two-dimensional materials. In particular, we show that any such medium whose response to an externally applied electromagnetic field is a geodesically flowing induced current, must be a superconductor. In this manner, we conclude that the underlying geometry of this type of media is that of a Lorentzian contact manifold. Moreover, we show that the macroscopic hallmark of their superconducting state is a purely topological condition equivalent to the geodesic nature of the induced current: the non-vanishing of its helicity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities. [ABSTRACT FROM AUTHOR]

For 0 < k < 1, a finite-type k-surface in 3-dimensional hyperbolic space is a complete, immersed surface of finite area and of constant extrinsic curvature equal to k. In Smith (2021), we showed that such surfaces have finite genus and finitely many cusp-like ends. Each of these cusps is asymptotic to an immersed cylinder of exponentially decaying radius about a complete geodesic and terminates at an ideal point which we call the extremity of the cusp. We show that every cusp of any finite-type k-surface has a well-defined axis, which we will call the Steiner geodesic of the cusp. One of the end-points of this axis is the extremity, and we will call the other, which constitutes new geometric data, the Steiner point of the cusp. We prove a new identity involving extremities and Steiner points in terms of Möbius invariant vector fields over the Riemann sphere. We define two new functionals over the space of finite-type k-surfaces. The first, which will be called the generalized volume, is defined by the integral of a certain well-chosen form, and extends to the non-embedded case the concept of volume of the set bounded by the surface. The second, which will be called the renormalized energy, is related to the integral of the mean curvature of the surface, and is well-defined up to a choice of Busemann function. Upon describing natural parametrizations of the strata of the space of finite-type k-surfaces by open complex manifolds, we prove a new Schläfli-type formula relating the extremities and Steiner points to the first order variations of the generalized volume and the renormalized energy. In particular, Möbius invariance of this formula yields the aforementioned identity. We conclude by studying some applications of this identity and Schläfli-type formula. [ABSTRACT FROM AUTHOR]

We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre & Ghrist (Etnyre, Ghrist 2000 Nonlinearity13, 441–458 (doi:10.1088/0951-7715/13/2/306)) can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that energy levels above the maximum of the potential energy of mechanical Hamiltonian systems can be viewed as stationary fluid flows, though the metric is not prescribed. In particular, we showcase the emblematic example of the n -body problem and focus on the Kepler problem. We explicitly construct a compatible Riemannian metric that makes the Kepler problem of celestial mechanics a stationary fluid flow (of Beltrami type) on a suitable manifold, the Kepler–Euler flow. [ABSTRACT FROM AUTHOR]

We present a Fefferman-type construction from Lagrangian contact to split-signature conformal structures and examine several related topics. In particular, we describe the canonical curves and their correspondence. We show that chains and null-chains of an integrable Lagrangian contact structure are the projections of null-geodesics of the Fefferman space. Employing the Fermat principle, we realize chains as geodesics of Kropina (pseudo-Finsler) metrics. Using recent rigidity results, we show that 'sufficiently many' chains determine the Lagrangian contact structure. Separately, we comment on Lagrangian contact structures induced by projective structures and the special case of dimension three. [ABSTRACT FROM AUTHOR]

Suppressing unwanted vibrations has been a major challenge for more than a century. Semi-active dampers offer a compromise between the high energy costs of active solutions and their increased flexibility. A nonlinear system that utilizes dry friction and piecewise defined contact geometries is used as the basis for a semi-active damper. Furthermore, a slow frequency-based control that does not solely rely on dissipation is considered and compared to the conventional Skyhook Control. Simulations show that the strategy is an effective approach for vibration reduction. [ABSTRACT FROM AUTHOR]

In water-based experiments exploring ultralow or super low friction, the implementation of a running-in period before reaching such states is necessary and important. However, the effect of the change in contact geometry has not been fully realized. In this paper, a series of running-in tests on a Si3N4 ball and a WC plate have been performed in glycerol–water mixtures with different concentrations. The shape of the wear scars and the chemical compositions of the worn surfaces were characterized in detail. A numerical EHD and mixed lubrication model was established to comprehensively analyze the effects of geometric profiles, surface roughness, and working/lubrication conditions on ultralow or super low sliding friction. The experiment and simulation results of the study have provided an in-depth understanding of the mechanism of super low friction of liquid lubricated sliding point contacts. [ABSTRACT FROM AUTHOR]

We state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincaré's dream of a scale-invariant description of the Universe. [ABSTRACT FROM AUTHOR]

In piled raft foundations, the bearing capacity is the result of the combination of the resistance of the pile group and the contribution of the contact between the pile cap and the soil. Although this contact contribution is still neglected, studies show that in certain cases, the load capacity directly absorbed by the pile cap can exceed the load absorbed by the pile group. Among the various factors that influence the behavior of piled raft foundations, the effect of contact geometry on the foundation has been inadequately researched. In this study, three-dimensional numerical analyses were conducted using the finite element method with the LCPC-CESAR software to investigate how pile cap–soil contact geometries affect the behavior of piled raft foundations. The net contact area, diameter, length, and number of piles were kept constant in all cases analyzed. Despite the complex interface of the LCPC-CESAR software, which hinders problem remodeling, validation securely demonstrated that this tool could replicate the behavior of piled raft foundations. The study results showed that, regardless of the spacing between the piles, the contact geometry does not affect the load–settlement curve of the system but significantly alters the distribution of loads among the foundation elements and the transfer of loads from the piles to the surrounding soil. When comparing pile cap geometries, it was observed that the square geometry supports a larger portion of the load compared to other geometries, likely due to better coverage of the pile inside the pile cap provided by this square configuration. [ABSTRACT FROM AUTHOR]

This paper aims to determine the effect of contact geometry on temperature distribution and thermal buckling in an in-wheel brake system. Numerical analysis is conducted to investigate the variation of temperature field distribution on the brake disc a different cover angles of the pad while maintaining the same moment of friction. Also, different positions of the pads on the disc are considered. To verify the simulation results, an analytical solution is derived. The results show that, for the same work done by the pads on the disc, the resulting temperature field distributions have various effects on the disc. Moreover, certain contact geometry was found to cause the braking temperature to exceed the critical temperature, leading to thermal buckling of the disc during braking. [ABSTRACT FROM AUTHOR]

We use a formulation of Noether's theorem for contact Hamiltonian systems to derive a relation between the thermodynamic entropy and the Noether invariant associated with time-translational symmetry. In the particular case of thermostatted systems at equilibrium, we show that the total entropy of the system plus the reservoir are conserved as a consequence thereof. Our results contribute to understanding thermodynamic entropy from a geometric point of view. [ABSTRACT FROM AUTHOR]

We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling through a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The 'contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework. [ABSTRACT FROM AUTHOR]

The effects of contact geometry and specific contact resistivity on In0.53Ga0.47As (InGaAs) and silicon (Si) nanoscale (18 nm channel length) n-channel FinFETs performance, and the effects of models thereof, are studied using a quantum-corrected semiclassical Monte Carlo method. Saddle/slot, raised source and drain (RSD), and reference end contacts are modeled. Both ideal perfectly injecting and absorbing contacts and those with more realistic specific contact resistivities are considered. Far-from-equilibrium degenerate statistics, quantum-confinement effects on carrier distributions in real-space and among energy valleys and on scattering, and quasiballistic transport are modeled. Silicon ⟨ 110 ⟩ channel and Si ⟨ 100 ⟩ channel FinFETs, multivalley InGaAs channel FinFETs with conventionally reported InGaAs energy valley offsets, and reference idealized Γ-valley-only InGaAs (Γ-InGaAs) channel FinFETs are simulated. Among our findings, InGaAs channel FinFETs are highly sensitive to modeled contact geometry and specific contact resistivity and to the band structure model, while Si channel FinFETs showed still significant but much less sensitivity to the contact models. For example, for idealized unity transmissivity contacts, Γ-InGaAs channel FinFETs performed best for all contact geometries, at least in terms of transconductance, and end contacts provided the best performance for all considered channel materials. For realistic contact resistivities, however, the results are essentially reversed. Silicon channel FinFETs performed best for all contact geometries, and saddle/slot and RSD contacts outperformed end contacts. [ABSTRACT FROM AUTHOR]

We study a nonequilibrium mean field Ising model in the low temperature phase regime, where metastable equilibrium states develop a cuspidal (spinodal) singularity. We focus on celebrated Glauber dynamics, and design a contact Hamiltonian flow which captures some of its rough features in this regime. We prove, however, that there is an inevitable discrepancy between the scaling laws for the relaxation time in the Glauber and the contact Hamiltonian dynamical systems. [ABSTRACT FROM AUTHOR]

In this note, we formulate and study a Hamilton–Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton–Jacobi theory consistently describes thermodynamic transformations on the space of externally controllable parameters or equivalently the space of equilibrium states. It turns out that in the Hamilton–Jacobi description, the choice of the principal function is not unique but, the resultant dynamical description for a given transformation remains the same irrespective of this choice. Some examples involving thermodynamic transformations of the ideal gas are discussed where the characteristic curves on the space of equilibrium states completely describe the dynamics. The geometric Hamilton–Jacobi formulation which has emerged recently is also discussed in the context of thermodynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study conformal Ricci soliton and almost conformal Ricci soliton within the framework of paracontact manifolds. Here, we have shown the characteristics of the soliton vector field and the nature of the manifold if para-Sasakian metric satisfies conformal Ricci soliton. We also demonstrate the feature of the soliton vector field V and scalar curvature when the para-Sasakian manifold admitting conformal Ricci soliton and vector field is pointwise collinear with the characteristic vector field ξ. Next, we prove that if a K-paracontact manifold confesses a gradient conformal Ricci soliton, then it is Einstein. Next, we show that a para-Sasakian metric reveals with an almost conformal Ricci soliton that is either Einstein or η -Einstein metric if the soliton vector field V is an infinitesimal contact transformation. Lastly, we decorate an example of conformal Ricci soliton on para-Sasakian manifold. [ABSTRACT FROM AUTHOR]

The contact geometries encountered in rolling element-outer race or inner race contacts in real bearings are not involved in conventional ball-on-flat disc configurations. However, the underlying lubricant replenishment mechanism induced by the contact conformity plays a significant role in maintaining a long-term operation of the rolling bearings. To reveal those replenishment mechanisms, the traditional flat disc is replaced by a grooved disc to reproduce the contact geometries. Additionally, a ball support structure consisting of dual arc-shaped rollers is employed to simulate the ball-inner race contact, aiming to explore the contributions of grease distributions to replenishment. The results show that the film thickness gradually diminishes to severe starvation states in the traditional contact configuration, while the lubrication states are efficiently improved as the ball-grooved or ball-arc shaped contact configuration is introduced, confirming the replenishment efficiency. The enhanced lubricant replenishment behaviors can be attributed to the high-strength shear exerted on the grease both at the inlet region and within the contacts where micro-slip occurs, as well as the surface tension and capillary force-induced lubricant replenishment. The findings of this study contribute to a comprehensive understanding of grease lubrication and replenishment in real bearings. [ABSTRACT FROM AUTHOR]

It is shown that the scalar curvature of a Yamabe soliton as a Sasakian manifold is constant and the soliton vector field is Killing. The same conclusion is shown to hold for a Yamabe soliton as a K-contact manifold M2n+1 if any one of the following conditions hold: (i) its scalar curvature is constant along the soliton vector field V, (ii) V is an eigenvector of the Ricci operator with eigenvalue 2n, (iii) V is gradient. [ABSTRACT FROM AUTHOR]

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, Hamiltonians can be defined that describe thermodynamic processes. [ABSTRACT FROM AUTHOR]

This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a new term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behavior of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric. [ABSTRACT FROM AUTHOR]

Tactile sensing plays an important role for robots' perception, but the existing tactile technologies have multiple limitations. Visual-tactile sensor (VTS) is a newly developed tactile detector; it perceives the contacting surface shape, or even more refined texture, by way of the contact deformation image captured by a camera. A conventional visual perception is usually formulated as a data processing. It suffers issues of cumbersome training set and complicated calibration procedures. A novel model-based depth perceptual scheme is proposed where a mapping from the image intensity to the contact geometry is mathematically formulated with an associated tailored fast solver. The hardware calibration requires single image only, leading to an outstanding algorithmic robustness. The non-uniformity of the illumination condition is embodied by the stereo model, resulting in a robust depth perception precision. Compression tests on a prototype VTS showed the method's capability in high-quality geometry reconstruction. Both contacting shape and texture were captured at a root-mean-square error down to a sub-millimeter level. The feasibility of the proposed in a pose estimation application is further experimentally validated. The associated tests yielded estimation errors that were all less than 3° in terms of spatial orientation and all less than 1mm in terms of translation. [ABSTRACT FROM AUTHOR]

Solving the wheel-turnout contact geometry is complex because the rail section is varying along its longitudinal position. Besides, a large yaw angle will occur, especially when the vehicle passes the switch panel in a diverging route. However, previous researches seldom considered the aforementioned factors simultaneously in performing wheel–rail local contact analysis. This paper therefore proposes a novel three-dimensional (3D) contact geometry method considering the combined effects of varying rail profiles and the yaw angle. This study uses S1002CN wheels and the switch panel of a 1:12 turnout as research objects to study the contact geometry, normal and tangential contact solution. The results indicate that the combined influences of rail profiles varying within the contact patch and the yaw angle on the contact solution are significant. The variable rail profiles obviously affect the position of the contact point. With a yaw angle, the normal gap, contact patch shape and stress distribution calculated by the novel 3D contact geometry method are asymmetric along the lateral and longitudinal directions, especially when the wheel flange contacts with a rail gauge corner. The proposed method can improve the accuracy of the wheel–rail contact solution and help predict rail damage in switch panels. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric. [ABSTRACT FROM AUTHOR]

Fused filament fabrication is an extrusion‐based additive manufacturing technology with relatively low‐cost equipment and a great variety of materials from standard to engineering grade. Multiple extrusion systems allow for new opportunities regarding the manufacturing of multi‐color and multi‐material parts. However, regular bond formation of part's bodies provided by the slicing tool offers good results regarding the resulting product's dimensional stability but poor mechanical properties. For this reason, this paper aims to investigate if the mechanical properties of compatible polymers can be enhanced by modifying the regular flat to a flat surface with different shape interfaces and an overlap degree between them. Furthermore, for a broader understanding of the bond formation, the design of the experiment comprises two groups referring to the material blend along with their melting ranges and join geometry, which is constrained with regard to nozzle output size. The results show that the mechanical properties of multi‐material bonds can be enhanced conveniently by adding an overlap degree between mating bodies. [ABSTRACT FROM AUTHOR]

Due to the inevitable flow-induced vibration and turbulent excitation in steam generator (SG), it is impossible to avoid fretting wear or impact between steam generator tubes (SGTs) and anti-vibration bars (AVBs). Therefore, the approach of this work was to simulate the real fretting problems between SGTs and AVBs. Thus, the impact-sliding fretting wear tests of 690TT alloy/405 stainless steel (405 SS) were investigated under various contact times in tube/plate configuration and tube/cylinder configuration in air at room temperature, respectively. The results indicated that the influences of contact geometry and contact time on the peak radial force (F rp) were insignificant, while the value of peak tangential force (F tp) was seen to increase with increasing contact time and was associated with the contribution of sliding wear to impact-sliding process. Meanwhile, the degree of wear damage increased with the increase of contact time, either line contact or point contact. The damage area of wear scar in tube/plate configuration was evidently larger than that of tube/cylinder configuration. Instead, the maximum wear depth of tube/cylinder configuration was larger than that of tube/plate configuration. Along the sliding direction, the "U" shape profiles were usually detected whether tube/plate configuration or tube/cylinder configuration. In general, both contact geometry and contact time had a direct influence on the behavior of wear debris, i.e., movement and oxidation. • The influences of contact geometry and contact time on peak radial force were insignificant. • The peak tangential force increased with increasing contact time and was associated with the contribution of sliding. • Contact geometry and contact time had a direct influence on the movement and oxidation of wear debris. [ABSTRACT FROM AUTHOR]

A transient mixed thermal elastohydrodynamic lubrication model of bearing considering the thermal effect and the changes in velocity, load, and contact geometry is proposed. Based on the bearing dynamic and lubrication analysis, the effects of bearing rotational speed and start-stop conditions on the dynamic behavior and lubrication performance are studied. Results show that when the bearing rotational speed exceeds a certain critical value, the increasing speed will reduce the film thickness, especially the outer raceway. The increasing bearing acceleration can cause a higher slide-roll ratio and film temperature at the initial start-up process. Compared with the start-up process, the lubrication change in the shut-down process has a similar opposite trend, but the overall lubrication performance is better. [ABSTRACT FROM AUTHOR]

We show that a decorated knot concordance from K 0 to K 1 induces an [ U ] -module homomorphism G : HFK − (− S 3 , K 0) → HFK − (− S 3 , K 1) , which preserves the Alexander and absolute ℤ 2 -Maslov gradings. Our construction generalizes the concordance maps induced on HFK ̂ studied by Juhász and Marengon [Concordance maps in knot Floer homology, Geom. Topol.20 (2016) 3623–3673], but uses the description of HFK − as a direct limit of maps between sutured Floer homology groups discovered by Etnyre et al. [Sutured Floer homology and invariants of Legendrian and transverse knots, Geom. Topol.21 (2017) 1469–1582]. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The use of detailed wheel/rail contact models has long been frustrated by the complicated preparations needed, to analyse the profiles for the local geometry and creep situation for the planar contact approach. A new software module is presented for this that automates the calculations in a generic way. Building on many components developed by others, this greatly simplifies the running of CONTACT for generic wheel/rail contact situations. Fully 3-d contact search algorithms are implemented. This uses the contact locus approach, that's simplified for wheel-on-rail situations and extended to wheel-on-roller contacts. A main characteristic of the new module is its extensive use of the multibody formalism, using markers to represent coordinate systems, using a newly designed, generic, object oriented-like software foundation. The contact geometry is analysed twice; first for the location of contact patches, and then for the local geometry of the contact patches. The contact search starts from profiles in their actual, overlapping positions. This yields the extent of interpenetration areas as needed for the potential contact definition. Different strategies may be employed for the tangent plane needed in the planar contact method. Creepages are formed automatically using rigid body kinematics, including wheel and track flexible bending. Numerical results illustrate the viability, generality, and robustness of the approach. The extension to conformal contacts is presented in an accompanying paper. [ABSTRACT FROM AUTHOR]

Given a surface S in a 3D contact sub-Riemannian manifold M, we investigate the metric structure induced on S by M, in the sense of length spaces. First, we define a coefficient K̂ at characteristic points that determines locally the characteristic foliation of S. Next, we identify some global conditions for the induced distance to be finite. In particular, we prove that the induced distance is finite for surfaces with the topology of a sphere embedded in a tight coorientable distribution, with isolated characteristic points. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate the almost quasi-Yamabe soliton and gradient almost quasi-Yamabe solitons under the framework of three-dimensional normal almost paracontact metric manifolds. [ABSTRACT FROM AUTHOR]

A first-order asymptotic analysis of the Griffith energy balance in the Johnson-Kendall-Roberts model of adhesive contact under non-symmetric perturbation of the contact geometry is presented. The pull-off force is evaluated in explicit form. A particular case of adhesive contact between a relatively stiff sphere and an elastic half-space is considered under the assumption that the sphere geometry is changed by the application of an arbitrary lateral normal surface loading. The effect of the sphere Poisson's ratio on controlling the adhesive pull-off force is considered. [ABSTRACT FROM AUTHOR]

• Expressions of geometrical-kinematic parameters in vertical surface grinding were derived. • A single-grain grinding force model was developed from the energy perspective. • Multiple-grain interactions in vertical surface grinding were analyzed. • The influence mechanisms of the wheel-workpiece contact geometry on grinding forces were revealed. Vertical surface grinding (VSG) is an effective method that can adapt to multiple machining tasks, including stock removal machining to get high productivity and finish machining to obtain high-quality surfaces. Force prediction can reveal some mechanisms in the VSG process, conducing to the improved machining quality and efficiency. This paper aims to develop a novel analytical force model considering the actual wheel-workpiece contact geometry (WWCG). In the modeling process, the cup grinding wheel was divided into many micro-cutting layers along the wheel axis, and the expressions of geometrical-kinematic parameters were derived to characterize the material removal at different positions of the primary grinding zone (PGZ). A single-grain grinding force model was proposed based on chip formation and plastic pile-up mechanisms from an energy perspective. Based on the analysis of multiple-grain interactions at each micro-cutting layer, equations of the local and total grinding forces in the VSG process were then derived by synthesizing the single-grain forces. Findings show that the developed model could accurately predict the magnitudes of total grinding forces and provide the distributions of local grinding forces. The WWCG variation could significantly affect the grinding forces by altering the material removal rate of different micro-cutting layers. This work provides a new method for predicting grinding forces and theoretical guidance for optimizing machining parameters and tailoring the edge profiles of cup grinding wheels to adapt to specific machining tasks. [Display omitted] [ABSTRACT FROM AUTHOR]

Can every physical system simulate any Turing machine? This is a classical problem that is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore [C. Moore, Nonlinearity 4, 199 (1991)] asked if hydrodynamics is capable of performing computations. More recently, Tao launched a program based on the Turing completeness of the Euler equations to address the blow-up problem in the Navier-Stokes equations. In this direction, the undecidability of some physical systems has been studied in recent years, from the quantum gap problem to quantum-field theories. To the best of our knowledge, the existence of undecidable particle paths of threedimensional fluid flows has remained an elusive open problem since Moore's works in the early 1990s. In this article, we construct a Turing complete stationary Euler flow on a Riemannian S3 and speculate on its implications concerning Tao's approach to the blow-up problem in the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g, V) with V as contact vector field on a Sasakian manifold (M, g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically fixed η-Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S2n+1. Further, we study H-contact manifold admitting a Riemann soliton (g, V) where V is pointwise collinear with ξ. [ABSTRACT FROM AUTHOR]

We have studied experimentally the conductive properties of single walled carbon nanotube (SWNT) based field-effect type devices, with different contact geometries at the connecting electrode. The device designs are asymmetric with one end of the SWNT having the metal electrode deposited on top and immersing it, while at the other end, the SWNT is on top of the electrode. The devices were made with either gold or palladium as electrode materials, of which the latter resulted in different behavior of the different contact types. This is argued to be caused by the existence of a thin insulating layer of surface adsorbents on the palladium, possibly Pd5O4, the effect of which is enhanced by the 1D nature of the contact area in the configuration with SWNT on top of electrode. [ABSTRACT FROM AUTHOR]

We prove that on a K-contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ. Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results. [ABSTRACT FROM AUTHOR]

Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green's function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries.We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its "closed" and "open" conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%. [ABSTRACT FROM AUTHOR]

We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalize the ordinary categories of smooth manifolds and vector bundles to account for a lack of choice of a preferred unit, which in standard differential geometry is always given by the global constant function 1. This is what we call the "unit-free" approach. After giving a characterization of local Lie brackets via their symbol maps, we apply our novel categorical language to review Jacobi manifolds and related notions such as Lichnerowicz brackets and Jacobi algebroids. The main advantage of our approach is that Jacobi geometry is recovered as the direct unit-free generalization of Poisson geometry, with all the familiar notions translating in a straightforward manner. We then apply this formalism to the question of whether there is a unit-free generalization of Hamiltonian mechanics. We identify the basic categorical structure of ordinary Hamiltonian mechanics to argue that it is indeed possible to find a unit-free analogue. This paper serves as a prelude to the investigation of dimensioned structures, an attempt at a general mathematical framework for the formal treatment of physical quantities and dimensional analysis. [ABSTRACT FROM AUTHOR]

By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems. [ABSTRACT FROM AUTHOR]

A topology is introduced on spaces of Legendrian submanifolds and groups of contactomorphisms. The definition is motivated by the Alexandrov topology in Lorentz geometry. [ABSTRACT FROM AUTHOR]

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. Keywords: : contact geometry, thermodynamics, optimal control, Hamiltonian systems, integrability [ABSTRACT FROM AUTHOR]

We analyze the transverse Kähler–Ricci flow equation on Sasaki-Einstein space Y p , q . Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki–Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein. [ABSTRACT FROM AUTHOR]

Given an almost paracontact structure (φ, ξ, η) on a pseudo- Riemannian manifold (M2n+1, g) of signature (n+1, n) we define a linear connection as being adapted if it parallelizes all its structural elements φ, η, ξ. We find the class of all adapted connections using the tools of derivations. The particular cases of para-Sasakian and para-Kenmotsu manifolds are detailed in order to compare with the Levi-Civita connec- tion of g and with the canonical connection of S. Zamkovoy from [24]. Also, we unify our framework with the almost contact geometry by using a parameter ε corresponding to ±1 and we find the class of linear connec- tions which provide the general admissible triples of covariant derivatives for (φ, η, ξ); in particular the Matzeu-Oproiu linear connection is ana- lyzed. We search applications of our computations to statistical and weak Frobenius structures. [ABSTRACT FROM AUTHOR]

A novel method to calculate single-particle fabric tensors and related geometric characteristics (contact, free and particle area, particle volume and contact centroid) of assemblies of spherical particles has been developed. A standard contact detection stage is used to identify overlapping particles. The shape of each contact region is obtained as the intersection of a circle, obtained in the absence of any contact impingement, and a convex polygon, determined by half-plane intersection based on directed lines obtained from the intersection of contact planes. An underlying power diagram is used to subdivide volume and area between particles, but calculations are performed particle-wise, resulting in an efficient algorithm with a structure ideally suited for parallelisation. Numerical tests performed on loose and dense particle assemblies and comparison (of single-particle free area and particle volume) with a reference method (POWERSASA) indicate that the method is robust and highly accurate. The method will be useful not only for geometric analysis but also as a basis for subsequent developments of strain measures and computational procedures for highly deformed granular materials. Moreover, it constitutes a viable alternative for calculation of solvent accessible surface areas, considering its robustness, efficiency and ease of parallelisation. [ABSTRACT FROM AUTHOR]