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We study coisotropic deformations of a compact regular coisotropic submanifold C in a contact manifold (M , ξ) . Our main result states that C is rigid among nearby coisotropic submanifolds whose characteristic foliation is diffeomorphic to that of C. When combined with a classical rigidity result for foliations, this yields conditions under which C is rigid among all nearby coisotropic submanifolds. [ABSTRACT FROM AUTHOR]

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]

An important tool to analyse the causal structure of a Lorentzian manifold is given by the Lorentzian distance function. We define a class of Lorentzian distance functions on the group of contactomorphisms of a closed contact manifold depending on the choice of a contact form. These distance functions are continuous with respect to the Hofer norm for contactomorphisms defined by Shelukhin [The Hofer norm of a contactomorphism, J. Symplectic Geom. 15 (2017) 1173–1208] and finite if and only if the group of contactomorphisms is orderable. To prove this, we show that intervals defined by the positivity relation are open with respect to the topology induced by the Hofer norm. For orderable Legendrian isotopy classes we show that the Chekanov-type metric defined in [D. Rosen and J. Zhang, Chekanov's dichotomy in contact topology, Math. Res. Lett. 27 (2020) 1165–1194] is nondegenerate. In this case, similar results hold for a Lorentzian distance functions on Legendrian isotopy classes. This leads to a natural class of metrics associated to a globally hyperbolic Lorentzian manifold such that its Cauchy hypersurface has a unit co-tangent bundle with orderable isotopy class of the fibres. [ABSTRACT FROM AUTHOR]

We show that, apart from degeneracies, determining a plane curve whose curvature depends on its position essentially consists of determining a null curve in the Lorentzian 3-space when the null tangent direction depends on its position. We use this point of view to investigate the intrinsic equations for the n-elastic curves. We show how the problem of prescribed null tangent direction in terms of the position can be solved by quadratures when the prescription exhibits sufficient symmetries. This problem is formalized in terms of a convenient contact 3-form. [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]

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]

We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated expansion rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov. We then study the symmetries that the existence of an invariant volume form yields on the geometry of an Anosov flow, from various viewpoints of the theory of contact hyperbolas, Reeb dynamics, and Liouville geometry, and give characterizations of when an Anosov flow is volume preserving, in terms of those theories. We finally use our study to show that the bi-contact surgery operations of Salmoiraghi [Surgery on Anosov flows using bi-contact geometry. Preprint , 2021, arXiv:2104.07109; and Goodman surgery and projectively Anosov flows. Preprint , 2022, arXiv:2202.01328] can be applied in an arbitrary small neighborhood of a periodic orbit of any Anosov flow. In particular, we conclude that the Goodman surgery of Anosov flows can be performed using the bi-contact surgery operations of Salmoiraghi [Goodman surgery and projectively Anosov flows. Preprint , 2022, arXiv:2202.01328]. [ABSTRACT FROM AUTHOR]

We construct non-compact contact manifolds containing compact Legendrians which can be displaced from their Reeb flow with arbitrarily small oscillation energy. We use this to show the Shelukhin-Chekanov-Hofer pseudo-metric considered by Rosen and Zhang (Math. Res. Lett. 27:1165–1193, 2020) is degenerate on the isotopy class of the constructed Legendrians. Other aspects related to oscillation energy of Legendrian isotopies are explored. [ABSTRACT FROM AUTHOR]

In this short note, we prove that singular Reeb vector fields associated with generic -contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) or an infinite number of escape orbits, where denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of -Beltrami vector fields that are not -Reeb. The proof is based on a more detailed analysis of the main result in [19]. [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]

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]

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]

We review recent studies of contact and thermodynamic geometry for black holes in AdS spacetimes in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure P = −Λ/8π and, subsequently a conjugate volume V, thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we review the contact geometry approach to thermodynamics in general and then consider thermodynamic metrics constructed as the Hessians of various thermodynamic potentials. We then study their correspondence to statistical ensembles for systems with two-dimensional spaces of equilibrium states. From the zeroes and divergences of the curvature scalar obtained from the metric, we carefully analyze the issue of ensemble non-equivalence and show certain complimentary behaviors in the description of a thermodynamic system. Following a thorough analysis of the familiar van der Waals system, we turn our attention to black holes in extended phase space. Considering the example of charged AdS black holes, we discuss the generic features of their thermodynamic geometry in detail. The relationship of the thermodynamic curvature(s) with critical points as well as microscopic interactions in black holes is also briefly explored. We finally set up the thermodynamic geometry for finite temperature gauge theories dual to black holes in AdS via holographic correspondence and comment on recent progress.

The thermodynamics of a conductive liquid is considered. The latter is described within the framework of contact geometry. The state and constitutive equations of the medium are obtained from the first principles and notion of symmetry under natural assumptions only. These thermodynamic relations are supplemented by the general laws of charge, mass, momentum, and energy conservation to form a complete system of partial differential equations that describe the motion of the media. Differential invariants of this system under the action of rotations and translations are studied. A complete set of such invariants is obtained. [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]

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]

The molecular scale magnetic proximity effect is proposed in single-molecule magnetic junctions (SMMJs) consisting of a dissociated amine-ended 1,4-benzenediamine (BDA) molecule coupled to two ferromagnetic Co electrodes. Our self-developed JunPy + Landau-Lifshitz-Gilbert simulation combined with first-principles calculation is employed to investigate the role of contact geometry in the magnetotransport properties of SMMJs with the choice of top, bridge, and hollow contact sites. The strong spinterface effect gives rise to distinct angular dependence of equilibrium field-like spin torque (FLST), asymmetric magnetic hysteresis loop and tunable exchange bias. From the analytical derivation of nonequilibrium Keldysh formalism, we believe that a promising way forward is to activate the multi-reflection process via the so-called molecular spinterface that will allow us to conquer as-yet unexplored magnetotransport properties of organic-based spintronics.

In this paper, we consider contact Hamiltonian description of 1D frictional dynamics with no conserved force. Friction forces that are monomials of velocity, and sum of two monomials are considered. For that purpose, quite general forms of contact Hamiltonians are taken into account. We conjecture that it is impossible to give a contact Hamiltonian description dissipative systems where the friction force is not in the form considered in this paper.

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.

This survey is based on lecture notes for an online mini-course taught for postgraduate students at UDELAR, Montevideo, Uruguay, in November 2020, remotely from the Mittag–Leffler Institute in Djursholm, Sweden. Lectures were recorded and are available online. [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]

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]

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 μ (COF) compared to the crosslinked surfaces, even achieving superlubricity (μ < 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. [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]