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We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton's principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology., 1 figure. Version accepted to Synthese. Substantive improvements and clarifications

Soft optical tactile sensors enable robots to manipulate deformable objects by capturing important features such as high-resolution contact geometry and estimations of object compliance. This work presents a variable stiffness soft tactile end-effector called StRETcH, a Soft to Resistive Elastic Tactile Hand, that is easily manufactured and integrated with a robotic arm. An elastic membrane is suspended between two robotic fingers, and a depth sensor capturing the deformations of the elastic membrane enables sub-millimeter accurate estimates of contact geometries. The parallel-jaw gripper varies the stiffness of the membrane by uni-axially stretching it, which controllably modulates StRETcH's effective modulus from approximately 4kPa to 9kPa. This work uses StRETcH to reconstruct the contact geometry of rigid and deformable objects, estimate the stiffness of four balloons filled with different substances, and manipulate dough into a desired shape., Comment: 8 pages, 8 figures, To be published in Proc. 2020 IEEE International Conference on Robotics and Automation (ICRA), expanded figures, added clarification for stiffness estimation (Sec. VI-B, paragraph 4)

In the presented work, tribological interactions of tetrahedral amorphous carbon (ta-C) coatings with variations of sp3 content have been systematically studied in the boundary lubrication regime with emphasis on fatty acid-based lubricants. Manifold phenomena regarding wear and friction have been observed that exceed the conventional understanding of lubricant-surface interaction. Distinct superlubricity behavior of ta-C was found when lubricated with glycerol or oleic acid. It was shown that both the acid function and the double bond in the lubricant molecules are essential features to achieve superlubricity. Superlubricity is not confined to self-mated ta-C surfaces, but also happens in contact to steel. The contact situation has important influence on tribological behavior. Wear rates change by 1–2 orders of magnitude by altering the contact geometry and loading conditions of an oleic-acid-lubricated ta-C/steel pairing. This ta-C wear phenomenon is attributed to tribochemical wear.

We study different norms on the group of contactomorphisms of a contact manifold. For every integers n greater than 0, using generating function techniques, we characterise some geodesics of the group of compactly supported contactomorphisms of R2n x S^1 endowed with its standard contact structure. We compute explicitely the norm of a big family of contactomorphisms of the unitary cotangent of the torus using a theorem of intersections between exact Lagrangians with the 0-section inside the cotangent. Finally we study the characteristic distribution on hypersurfaces lying inside the contactification of an exact symplectic manifold. It allows us to define a new set of values for open domains of the contact manifold considered. This set of values contains contact invariants and generalise the notion of the spectrum of an open domain in an exact symplectic manifold., Nous étudions différentes normes sur le groupe des contactomorphismes d’une variété de contact. Pour tout entier n plus grand que 1, grâce à la technique des fonctions génératrices, nous caractérisons certaines géodésiques du groupe des contactomorphismes à support compact de R^2n x S^1 que l’on munit de sa structure de contact standard. Nous calculons explicitement la norme d’une grande famille de contactomorphismes du cotangent unitaire du tore en utilisant un théorème d’intersections de lagrangiennes exactes du cotangent avec la section nulle. Enfin nous étudions la distribution caractéristique des hypersurfaces contenues dans la contactisation d’une variété symplectique exacte. Cela nous permet de définir un ensemble de valeurs pour les ouverts de la variété de contact considérée. Cet ensemble de valeurs contient des invariants de contact et généralise la notion du spectre d’un ouvert d’une variété symplectique exacte.

Superalloy coatings of the CoMoCrSi family (e.g. Tribaloy® T800) are applied to mitigate wear effects at high temperature. These coatings are extensively used on the contact surfaces of the shroud of turbine blades. If severe wear occurs on these contact surfaces the blade interlocking decreases, reducing the stiffness of the assembly, altering its dynamic behaviour, and increasing the risk of fatigue failure. Fretting is the expected damage mechanics on these mating surfaces. The study presented in this paper investigates the fretting damage mechanism of interfaces coated with CoMoCrSi alloys. The experimental plan includes fifteen combinations of the test parameters: two contact geometries, three deposition processes, four temperatures, three normal loads and three strokes. Wear at different number of cycles was also explored. Moreover, two types of contact geometries were investigated, namely point contact (sphere-on-flat) and flat-on-flat. The friction coefficient was computed using the hysteresis loops measured during the fretting tests. The topography of the contact surfaces was measured at different fretting wear cycles to estimate the volume loss. Wear grooves were observed by scanning electron microscopy. Results of point contact experiments at room temperature exhibited a steady friction coefficient independent of the normal load. Wear volumes showed a sharp increasing in wear rate at high dissipated energy while the trend was linear at lower dissipated energy. Oxidation was found more dependent on substrate than on temperature, stroke and wear cycles. Wear volumes and wear rate on flat-on-flat specimens coated with welded T800 were higher at 400 C than at room temperature and at high temperature (800 C). At room temperature, wear volumes of welded T800 applied by single layer were much higher than in dual layer. At room temperature and at low dissipated energy the wear rate of the point contact geometry was lower than flat-on-flat. At high energy, the wear rate of point contact tends to the flat-on-flat wear rate.

Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in externally and internally driven macroscopic systems that are far from equilibrium and are investigated on microscopic, mesoscopic, and macroscopic levels. In this paper we formulate the multiscale thermodynamics, explain its origin, and illustrate it in mesoscopic dynamics that combines levels., 53 pages no figures

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 $\widehat K$ 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., 24 pages, 15 figures

V delu se ukvarjamo s kontaktnimi strukturami na gladkih mnogoterostih, tj. popolnoma neintegrabilnimi podsvežnji kodimenzije ena v tangentnem svežnju dane mnogoterosti. Obravnavamo Grayev izrek, ki pravi, da so članice gladke družine kontaktnih struktur na sklenjeni mnogoterosti med seboj kontaktomorfne. Dokažemo Darbouxov izrek o lokalni ekvivalenci kontaktnih struktur na mnogoterostih iste razsežnosti. Slednji je poseben primer izreka o okolicah sklenjenih izotropnih podmnogoterosti v dani ambientni mnogoterosti. Difeomorfni izotropni podmnogoterosti v različnih mnogoterostih imata namreč kontaktomorfni cevasti okolici, čim sta njuna konformna simplektična normalna svežnja izomorfna. Pogoj je trivialno izpolnjen za Legendrove podmnogoterosti, kar napelje na podrobnejšo obravnavo krivulj in vozlov v tri-mnogoterostih. Pokažemo, da lahko poljubno zvezno krivuljo aproksimiramo z Legendrovo v C0-topologiji. Dokažemo tudi obstoj kontaktnih struktur na sklenjenih in orientabilnih trirazsežnih mnogoterostih. Definiramo pojem zavite kontaktne strukture na trirazsežni mnogoterosti in obravnavamo njene osnovne lastnosti. In this thesis we study contact structures on smooth manifolds, i. e. completely nonintegrable subbundles of codimension one of the tangent bundle. We prove Gray's theorem, which states that the members of a smooth family of contact structures on a closed manifold are pairwise contactomorphic. Darboux's theorem, which we also prove, states that contact manifolds have no local invariants, apart from dimension. It is itself a special case of the isotropic neighbourhood theorem, which allows us to identify tubular neighbourhoods of diffeomorphic isotropic submanifolds in two different contact manifolds, provided they have isomorphic conformal symplectic normal bundles. This condition holds trivially for Legendrian submanifolds, which in turn allows a more detailed study of curves and knots in three-manifolds. We show that any continuous curve can be approximated with a Legendrian one in C0-topology. We prove that closed orientable three manifolds always admit contact structures. We define overtwisted contact structures on three-manifolds and study their basic properties.

Weyl semimetal TaAs, congenially accommodating the massless Weyl fermions, furnishes a platform to observe a spontaneous breaking of either the time-reversal or the inversion symmetry and the concurrent genesis of pairs of Weyl nodes with significant topological durability. Former experimental analysis, which reveals that the near-zero spin-polarization of bulk TaAs, experiences a boost in proximity of point-contacts of non-magnetic metals along with the associated tip-induced superconductivity, provides the impetus to study the large-area stacked interfaces of TaAs with noble metals like Au and Ag. The primary outcomes of the present work can be listed as follows: (1) First-principles calculations on the interfacial systems have manifested an increment of the interface-induced spin-polarization and contact-induced transport spin-polarization of TaAs in proximity of noble metals; (2) In contrast to the single interface, for vertically stacked cases, the broken inversion symmetry of the system introduces a z-directional band-dispersion, resulting in an energetically separated series of non-degenerate band crossings. The simultaneous presence of such band-crossings and spin-polarization indicated the coexistence of both broken time reversal and inversion symmetries for metal-semimetal stacked interfaces; (3) quantum transport calculations on different device geometries reveal the importance of contact geometry for spin-transport in TaAs devices. Lateral contacts are found to be more effective in obtaining a uniform spin transport and larger transport spin polarization; (4) the phonon dispersion behaviour of TaAs displays a closure of band-gap with the associated increase of phonon-density of states for the acoustic modes in proximity of lateral contacts of noble metals.

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)&times, S1.

Deep brain stimulation (DBS) involves activation of targeted brain tissue through implantable electrodes to treat neurological disorders. In this study, two novel electrode designs, recessed flat-contact and recessed curvature-contact models were developed where the electrode contacts were recessed to a specified depth to improve directional selectivity. Furthermore, the contact geometry was also modified for the recessed curvature-contact model in order to obtain a hemispherical configuration that will help increase current steering and reduce the propensity of tissue damage. The predicted tissue damage produced by these models were compared to the standard array model using the Shannon tissue damage model criteria. Furthermore, the volume of tissue activated by each of the electrode models was analyzed, and the radial projection relative to the total projection of each geometry was determined as a measure of directional selectivity. Based on the trends observed in the current density, tissue damage, and volume of tissue activated (VTA) analyses, it is inferred that the recessed contact electrode geometries help improve directional selectivity and safety of DBS.

In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential forms, called $b^m$-contact forms, having an associated critical hypersurface $Z$. We provide several constructions, prove local normal forms, and study the induced structure on the critical hypersurface. The topology of those are related to smooth contact structures through a desingularization technique. The problem of existence of $b^m$-contact structures on a given manifold is also tackled in this paper. We prove that a connected component of a convex hypersurface of a contact manifold can be realized as a connected component of the critical set of a $b^m$-contact structure. In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential forms, called $b^m$-contact forms, having an associated critical hypersurface $Z$. We provide several constructions, prove local normal forms, and study the induced structure on the critical hypersurface. The topology of those are related to smooth contact structures through a desingularization technique. The problem of existence of $b^m$-contact structures on a given manifold is also tackled in this paper. We prove that a connected component of a convex hypersurface of a contact manifold can be realized as a connected component of the critical set of a $b^m$-contact structure. In particular, in the $3$-dimensional case, this construction yields the existence of a generic set of surfaces $Z$ such that the pair $(M,Z)$ is a $b^{2k}$-contact manifold and $Z$ is its critical hypersurface. {As a consequence of the desingularization techniques in \cite{gmw1}, we prove the existence of folded contact forms on any almost contact manifold.} Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA AcademiaPrize 2016. C ́edric Oms is supported by an AFR-Ph.D. grant ofFNR - Luxembourg National Research Fund. Eva Mi-randa and C ́edric Oms are partially supported by the grants reference number MTM2015-69135-P (MINECO/FEDER)and reference number 2017SGR932 (AGAUR). Eva Miranda was supported by aChaire d’Excellenceof theFondationSciences Math ́ematiques de Pariswhen this project started and this work has been supported bya public grant overseenby the French National Research Agency (ANR) as part of the“Investissements d’Avenir”program (reference: ANR-10-LABX-0098). This material is based upon work supported by the National Science Foundation under Grant No.DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, Califor-nia, during the Fall 2018 semester

Starting from a contact Hamiltonian description of Lìenard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime.

Strongly confined environments (confined dimensions between 1–100 nm) represent unique challenges and opportunities for understanding and manipulating molecular behavior due to the significant effects of electric double layers, high surface-area to volume ratios, and other phenomena at the nanoscale. Convex Lens-induced Confinement (CLiC) can be used to analyze the dynamics of individual molecules or particles confined in a planar slit geometry with continuously varying gap thickness. We describe an interferometry-based method for precise measurement of the slit pore geometry. Specifically, this approach permitted accurate characterization of separation distances as small as 5 nm, with 1 nm precision, without a priori knowledge or assumptions about the contact geometry, as well as a greatly simplified experimental setup that required only a lens, coverslip, and inverted microscope. The interferometry-based measurement of gap height offered a distinct advantage over conventional fluorescent dye-based methods; e.g., accurate interferometric height measurements were made at low gap heights regardless of solution conditions, while the concentration of fluorescent dye was significantly impacted by solution conditions such as ionic strength or pH. The accuracy of the interferometric measurements was demonstrated by comparing the experimentally measured concentration of a charged fluorescent dye as a function of gap thickness with dye concentration profiles calculated using Debye–Hückel theory. Accurate characterization of nanoscale gap thickness will enable researchers to study a variety of practical and biologically relevant systems within the CLiC geometry.

This article is based on a talk at the RIEMain in Contact conference in Cagliari, Italy in honor of the 78th birthday of David Blair one of the founders of modern Riemannian contact geometry. The present article is a survey of a special type of Riemannian contact structure known as Sasakian geometry. An ultimate goal of this survey is to understand the moduli of classes of Sasakian structures as well as the moduli of extremal and constant scalar curvature Sasaki metrics, and in particular the moduli of Sasaki-Einstein metrics., 48 pages

This survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in dedicating the conference to him. Georges Reeb once made the comment that the mere existence of a contact form on a manifold should in some sense “tighten up” the manifold. The statement seemed quite pertinent for a conference that brought together both geometers and topologists working on contact manifolds, whether in terms of “tight” vs. “overtwisted” or whether an associated metric should have some positive curvature. The first section will lay down the basic definitions and examples of the subject of contact metric manifolds. The second section will be a continuation of the first discussing tangent sphere bundles, contact structures on 3-dimensional Lie groups and a brief treatment of submanifolds. Section III will be devoted to the curvature of contact metric manifolds. Section IV will discuss complex contact manifolds and some older style topology. Section V treats curvature functionals and Ricci solitons. A sixth section has been added giving a discussion of the question of whether a Riemannian metric g can be an associated metric for more than one contact structure; at the conference this was an addendum to the third lecture.

Gear hone is a special tool used for roll finishing of lateral faces of hardened gear teeth. Over time, penetration of abrasive grains into the metal, wear and breaking in of the hone material, contact and bending deformation of the hone teeth, especially if an elastic binding agent is used, lead to changing the tooth contact geometry, i.e. a point contact turns into an elliptical contact. The gear hone tooth deformation is a function of the contact point height, i.e. for contact points closer to the tooth top, the deformation is many times larger than that occurring for contact points closer to the tooth bottom. It affects the specific sliding ratio between the meshing hone and the workpiece. Meanwhile, slight equalization of the specific sliding along the tooth height occurs. Comparable deformations, errors and metal removal rates applicable to the gear hone and the workpiece would contribute to the effectiveness of the error reduction measures. The elasticity of the tool’s composite material must be duly considered in calculating the geometry, selecting the compound composition and assessing the applicability of gear hones.

We prove a version of the Arnol'd conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian $L$ which has non-zero Morse-Novikov homology for the restriction of the Lee form $\beta$ cannot be disjoined from itself by a $C^0$-small Hamiltonian isotopy. Furthermore for generic such isotopies the number of intersection points equals at least the sum of the free Betti numbers of the Morse-Novikov homology of $\beta$. We also give a short exposition of conformal symplectic geometry, aimed at readers who are familiar with (standard) symplectic or contact geometry., Comment: 15 pages. v2 fixes some attribution issues, updates bibliography and corrects some typos. v3: major strengthening of the main theorem (Theorem 1.1), plus small corrections

Subsidence of implants into bone is a major source of morbidity. The underlying mechanics of the phenomenon are not clear, but are likely related to interactions between contact stresses and the underlying porous trabecular bone structure. To gain insight into these interactions, we studied the penetration of three-dimensional (3D)-printed indenters with systematically varying geometries into Sawbones® foam substrates and isolated the effects of contact geometry from those of overall contact size and area. When size, contact area, and indented material stiffness and strength are controlled for, we show that resistance to penetration is in fact a function of topology only. Indenters with greater line contact lengths support higher subsidence loads in compression. These results have direct implications for the design of implants to resist subsidence into bone.

Energy efficiency and functional reliability are the two key requirements in the design of high-performance transmissions. Therefore, a representative analysis replicating real operating conditions is essential. This paper presents the thermoelastohydrodynamic lubrication (TEHL) of meshing spur gear teeth of high-performance racing transmission systems, where high generated contact pressures and lubricant shear lead to non-Newtonian traction. The determination of the input contact geometry of meshing pairs as well as contact kinematics are essential steps for representative TEHL. These are incorporated in the current analysis through the use of Lubricated Loaded Tooth Contact Analysis (LLTCA), which is far more realistic than the traditional Tooth Contact Analysis (TCA). In addition, the effects of lubricant and flash surface temperature rise of contacting pairs, leading to the thermal thinning of lubricant, are taken into account using a thermal network model. Furthermore, high-speed contact kinematics lead to shear thinning of the lubricant and reduce the film thickness under non-Newtonian traction. This comprehensive approach based on established TEHL analysis, particularly including the effect of LLTCA on the TEHL of spur gears, has not hitherto been reported in literature.

To investigate the effects of the contact geometry, interfacial friction, and substrate recovery on the behavior of polymer scratching using a conical tip, an analytical model is proposed. The normal stress acting on the contact surface between the tip and the substrate is described as a function of the included angle θ, representing the angle between two planes across the axis of the conical tip, and the attack angle β, representing the angle between the conical surface and the substrate material surface. The effects of the rear contact geometry on the scratch friction between the tip and substrate, represented by recovery angle φ, owing to the instantaneous elastic recovery of the polymer substrate, are also introduced. Validated by the experimental and numerical results from the literature, the proposed analytical model can describe well the scratch coefficient of friction (SCOF), which is defined as the ratio of the tangential force to the normal force. Meaningful guidance is provided to understand the scratch friction behavior.

Laser induced transient current technique (LI-TCT) was proven to be a successful tool for measuring at the same time carrier lifetime, carrier mobility , and electric field distribution in X- and gamma ray detectors with plain contacts on opposite surfaces. Unfortunately, the most performing detectors exploit more complicated contact geometries that, hindering hole contribution to signal formation, allow a much better spectroscopy . In this paper, a LI-TCT based method is presented, for the determination of transport parameters as well as electric field distribution directly in single carrier devices. The method’s validity is demonstrated in twin CdZnTe detectors having similar material properties, but different weighting potentials.

This study investigates the thermal response of titanium alloy fretting sliding through a numerical approach with the consideration of the friction dissipation, plastic dissipation, surface roughness and wear. The fretting sliding of a cylindrical pad on a specimen with surface roughness is modeled to predict the temperature distribution, the evolution of the wear profile, and the fields of surface and subsurface stresses. Specifically, a thermo-elasto-plastic constitutive model considering the thermal-induced softening of material properties is developed to evaluate the contact pressure and the tangential stress on the surfaces as well as the subsurface stresses in the contacting components. The friction and plastic energy dissipations function together as the heat source to cause the temperature rise in the contact zone. A modified Archard model is used to predict the wear profile of the contact surface and change the contact geometry. The models are then incorporated in the finite element analysis of the fretting sliding to evaluate the thermal response. The influences of the plastic dissipation and the surface roughness on the temperature rise in the fretting sliding are discussed.

Dynamic contact resistance measurement (DRM) is an effective technique to evaluate the contact conditions of high voltage SF 6 circuit breaker. However, the relations between DRM characteristics and contact performance remain ambiguous, the influence of the electrical stress on the DRM curves is equivocal as well, and there is no contact erosion evaluation method based on DRM. To investigate the relations between DRM characteristics and contact erosion, the DRM results of high voltage SF 6 circuit breaker at various degrees of erosion obtained from the designed experiments are presented. The experiments demonstrate that with the degradation of the contacts, the average arcing contact resistance ( R a ) increases, and the arcing contact wipe ( D a ) decreases. Then, the simulation of the erosion test is performed to analyse the relations between R a and D a and the contact performance. The results show that with the decrease of R a , the threshold of D a to ensure the success of the current commuting from the main contacts to the arcing contacts becomes shorter. Moreover, the influence of the electrical stress on R a and D a are investigated. Results demonstrate that R a reflects the influence of arc by-products and contact geometry caused by electrical stress, and that D a reflects the influence of the interrupted current, the arcing time, the contact geometry, and the contact material. Finally, an evaluation method of the contact erosion for SF 6 circuit breaker based on DRM is proposed.

Riemannian and contact geometry formalisms are used to study the fundamental equation of electromagnetic radiation-like systems, obeying a Stefan–Boltzmann’s-like law. The vanishing of metric determinant is used for classifying what kind of systems cannot represent a possible generalization of blackbody-like systems. In addition, thermodynamic curvature scalar R is evaluated for a thermodynamic metric, giving R = 0 , which validates the non-interaction hypothesis stating that the scalar curvature vanishes for non-interacting systems.

The friction properties of a dilute solution of block copolymer additives in poly-α-olefin (PAO) confined between mica surfaces were investigated using the surface forces apparatus. Friction measurements were made for poly(11-acrylamidoundecanoic acid)-block-poly(alkyl methacrylate)-block-poly(11-acrylamidoundecanoic acid) with an alkyl chain length of C12 (A5L946A5) in the poly(alkyl methacrylate) blocks. The results were compared to those for a PAO solution of a similar triblock copolymer with an alkyl chain length of C18 (A5S992A5) examined in our previous work (Yamada et al., Langmuir 2015). The friction coefficient μ for A5L946A5/PAO was approximately 0.5, which was one or two orders of magnitude larger than that for A5S992A5/PAO (μ of 0.002–0.039). Detailed analysis of the dynamic thickness and contact geometry enabled us to investigate the difference in the friction reduction abilities of the two additives. A5L946A5 has a high affinity to PAO and the molecules have expanded conformation in PAO; extensive chain entanglement effect results in the formation of a thick and viscous lubricant layer, which gives rise to high friction. On the other hand, A5S992A5 has low affinity to PAO, and the shrunken A5S992A5 molecules adsorbed on the surfaces form a rigid slip plane at the interface, which gives rise to low friction. Our results provide insights into the oil/additive combinations used for low friction in oil-based lubrication. The friction properties of a dilute solution of block copolymer additives in a base lubricant oil confined between mica surfaces were investigated using the surface forces apparatus. Friction force, sliding film thickness, and contact geometry were evaluated in detail, and the results were compared to those of the solutions of a different block copolymer additive having similar molecular structure. The relationship between the chemical structure of additives, confined structures between surfaces, and friction mechanisms were discussed, which shed new light of the design of low-friction surfaces in oil-based lubrication.

In the last two decades, significant progress has been made on developing new nanoscale mechanical property measurement techniques including instrumented indentation and atomic force microscopy based techniques. The changes in the tip-sample contact mechanics during measurements uniquely modify the displacement and force sensed by a measurement sensor and much effort is dedicated to correctly retrieve the sample mechanical properties from the measured signal. It turns out that in many cases, for the sake of simplicity, a simple contact mechanics model is adopted by overlooking the complexity of the actual contact geometry. In this work, a newly developed matrix formulation is used to solve the stress and strain equations for samples with edge geometries. Such sample geometries are often encountered in today’s nanoscale integrated electronics in the form of high-aspect-ratio fins with widths in the range of tens of nanometers. In the matrix formulation, the fin geometries can be easily modeled as adjacent overlapped half-spaces and the contact problem can be solved by a numerical implementation of the conjugate gradient method. This method is very versatile in terms of contact geometry and contact interaction, either non-adhesive or adhesive. The discussion will incorporate a few model examples that are relevant for the nanoscale mechanics investigated by intermittent contact resonance AFM (ICR-AFM) on low-k dielectric fins of high-aspect-ratio. In such ICR-AFM measurements, distinct dependence of the contact stiffness was observed as a function of the applied force and distance from the edges of the fins. These dependences were correctly predicted by the model and used to retrieve the mechanical changes undergone by fins during fabrication and processing.

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics., Comment: 7 pages, 1 figure, LaTeX, references added, journal version

Wheel flat is one kind of railway train wheelset defects. It has great influence on wheel/rail dynamics and damages. In most of the presented studies, wheel/rail impact velocity or rolling radius v...

Numerous biomimetic structures made from elastomeric materials have been developed to produce enhancement in properties such as adhesion, static friction, and sliding friction. As a property, one expects adhesion to be represented by an energy per unit area that is usually sensitive to the combination of shear and normal stresses at the crack front but is otherwise dependent only on the two elastic materials that meet at the interface. More specifically, one would expect that adhesion measured by indentation (a popular and convenient technique) could be used to predict adhesion hysteresis in the more practically important rolling geometry. Previously, a structure with a film-terminated fibrillar geometry exhibited dramatic enhancement of adhesion by a crack-trapping mechanism during indentation with a rigid sphere. Roughly isotropic structures such as the fibrillar geometry show a strong correlation between adhesion enhancement in indentation versus adhesion hysteresis in rolling. However, anisotropic structures, such as a film-terminated ridge-channel geometry, surprisingly show a dramatic divergence between adhesion measured by indentation versus rolling. We study this experimentally and theoretically, first comparing the adhesion of the anisotropic ridge-channel structure to the roughly isotropic fibrillar structure during indentation with a rigid sphere, where only the isotropic structure shows adhesion enhancement. Second, we examine in more detail the anomalous anisotropic film-terminated ridge-channel structure during indentation with a rigid sphere versus rolling to show why these structures show a dramatic adhesion enhancement for the rolling case and no adhesion enhancement for indentation.

The friction behavior of soft, aqueous, biotribological contacts depends on contact geometry, speed, and pressure. Previous efforts to measure the surface profile of soft sliding contacts have been stymied by the matching index of refraction of aqueous materials submerged in water. Here, hydrogel surface deformations were imaged using confocal microscopy to experimentally investigate the contact geometry as a function of sliding speed. In situ fluorescence confocal microscopy measurements of the contact deformation during unidirectional friction experiments revealed the existence of a front/back asymmetry that increased with increasing sliding speed. A polyacrylamide hydrogel disk (96.5% water) was polymerized with fluorescent dyes and used as a rotating countersample below a polished glass hemispherical pin (1 mm radius of curvature). All experiments were performed submerged in a dilute (0.7 wt%) suspension of 1 μm red fluorescent microspheres in ultrapure water. Imaging of the contact was performed using a confocal microscope in situ with unidirectional sliding at 0.1, 1, 10, and 100 mm/s. The friction coefficient increased monotonically with increasing speed from μ ~ 0.04 at 0.1 mm/s to μ ~ 0.20 at 100 mm/s. All imaging was performed relative to the stationary glass probe under steady-state conditions. The contact line measured by connecting the leading and exiting contact points was nearly perpendicular to the loading direction at 0.1 mm/s sliding speed, but distorted as sliding speed increased. Consistent with the theories of viscoelastic contributions to polymer friction, the tangent of the contact-line angle correlated with friction.

When we touch an object, complex frictional forces are produced, aiding us in perceiving surface features that help to identify the object at hand, and also facilitating grasping and manipulation. However, even during controlled tactile exploration, sliding friction forces fluctuate greatly, and it is unclear how they relate to the surface topography or mechanics of contact with the finger. We investigated the sliding contact between the finger and different relief surfaces, using high-speed video and force measurements. Informed by these experiments, we developed a friction force model that accounts for surface shape and contact mechanical effects, and is able to predict sliding friction forces for different surfaces and exploration speeds. We also observed that local regions of disconnection between the finger and surface develop near high relief features, due to the stiffness of the finger tissues. Every tested surface had regions that were never contacted by the finger; we refer to these as “tactile blind spots”. The results elucidate friction force production during tactile exploration, may aid efforts to connect sensory and motor function of the hand to properties of touched objects, and provide crucial knowledge to inform the rendering of realistic experiences of touch contact in virtual reality.

A procedure for the design of contact systems with consideration of the electrical and tribological properties is presented. Wear and electrical tests under variation of the parameters coating system, contact geometry, and contact force are performed with the aim to find optimum contact parameters and to use the results for calculations. Example calculations are carried out, and the results are summarized in selection diagrams, which can be used in the product development as the basis for the design of plug-in connectors.

An appropriate clearance is required between mating gears for effective power transmission. In the present work, the effect of radial misalignment on mild wear of spur gear is modeled and simulated. The changes in the gear tooth contact geometry due to progressive wear have also been accounted in the model. The simulation results show that in the pinion dedendum region, pressure angle increases, while the contact pressure and wear depth decrease with increase in number of wear cycles. As far as the effect of radial misalignment is concerned, contact pressure decreases and wear depth increases with the increase in misalignment. In the pinion addendum region, pressure angle and wear depth increase with the increase in wear cycles, while the contact pressure and wear depth decrease with the increase in misalignment. The pressure angle and pitch point change from initial 20° (23rd pitch point) to 20.95° (26th pitch point) and 21.86° (28th pitch point) due to 0.5- and 1-mm radial misalignment, respectively. The wear depths after 50,000 wear cycles are − 1.32 × 10−2 μm, − 3.33 × 10−3 μm and − 4.39 × 10−4 μm at 23rd, 26th and 28th pitch points, respectively. The effect of radial misalignment on backlash, pressure angle, pitch point, contact ratio, double tooth contact region and speed ratio is also discussed.

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form.

Embedded contact homology (ECH) capacities were defined by Hutchings and provide a family of obstructions to embeddings of four-dimensional symplectic manifolds. In Part I of this thesis, we prove that for a four-dimensional Liouville domain with all ECH capacities finite, the asymptotics of the ECH capacities recover the symplectic volume. This was joint work with Daniel Cristofaro-Gardiner and Michael Hutchings. In Part II of this thesis, we construct topological absolute gradings in Heegaard Floer homology and bordered Floer homology that satify all of the expected properties. This was joint work with Yang Huang. We also show that the isomorphism between Heegaard Floer homology and ECH preserves the absolute gradings.

A new framework which describes the role of three key processes in fretting wear of metals is proposed, with these three processes being: (i) oxygen transport into the contact; (ii) formation of oxide-based wear debris in the contact and (iii) ejection of the wear debris from the contact. Based upon a physical understanding, rate equations for the three key processes are proposed, which provide a basis for the influence of test parameters (such as contact geometry, applied load, slip amplitude, fretting frequency etc) on the three rates to be understood. To maintain system equilibrium in steady-state fretting, the three processes must operate at the same rate as each other (debris cannot be ejected from the contact faster than it is formed, and debris cannot be formed faster than it is ejected). Accordingly, the observed wear rate is the rate of the process with the lowest rate of the three processes, with this process being termed the rate-determining process. The effect of test parameters on the three key processes differs, and thus the effect of changes in any test parameter on the observed rate of wear will itself be dependent upon which of the three processes is rate-determining. A number of assumptions have been made in deriving the equations which describe the key processes and it is recognised that these equations themselves may be refined in light of future research; however, any such revised equations can simply replace those proposed as part of the rate-determining process framework. The framework can be applied to both conforming and non-conforming contact geometries. In tests with non-conforming contact geometries, the contact size increases with wear; since it is proposed that the rates of two of the three processes (oxygen transport and debris ejection) are dependent upon the size of the contact, the rate determining process can change during such a test and the rate of wear will continually fall when either of these processes are rate-determining. This complexity means that the evolution of the wear volume can only be evaluated numerically through the use of a time-marching analysis in such cases. In contrast, in tests with conforming contact geometries, the contact size does not change as wear occurs, and so there will be no changes in the rate-determining process as wear proceeds. It is recognised that this framework addresses wear under steady-state conditions and does not consider the initial period of exposure where steady-state conditions are being developed. In the case of conforming contacts where the contact size is large, the duration of the initial transient period may be substantial and may form a significant proportion of the test duration or component lifetime. This needs to be recognised both in the design of tests and in the application of this framework.