3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

Critical discontinuous phase transition in the threshold contact process

We analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously. We show by means of Monte Carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter, in accordance with the Gibbs phase rule, and that the discontinuous transition exhibits critical behavior. The simulations were performed by using boundary conditions in which the sites of the border of the lattice are permanently occupied by particles.

Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Who gets the cats...you or me? Analyzing contact and residence issues regarding pets upon divorce or separation

Mills and Akers outline the statistical incidence of pet ownership and people's need for domestic pets, discuss ownership or property rights in domestic pets, outline the criteria used by the courts when ruling on implied contact and residence rights regarding domestic pets upon the irretrievable breakdown between the "owners" of the particular pets, and highlight both the shortcomings in the existing law and possible means of overcoming those shortcomings.

Identifying Heel Contact and Toe-Off Using Forceplate Thresholds With a Range of Digital-Filter Cutoff Frequencies

Analysis of human gait requires accurate measurement of foot-ground contact, often determined using either foot-ground reaction force thresholds or kinematic data. This study examined the differences in calculating event times across five vertical force thresholds and validated a vertical acceleration-based algorithm as a measure of heel contact and toe-off.

Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body

Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-`a-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green’s function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.

Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming

To quantify the frictional behaviour in sheet forming operations, several laboratory experiments which simulate the real forming conditions are performed. The Bending Under Tension Test is one such experiment which is often used to represent the frictional flow of sheet material around a die or a punch radius. Different mathematical representations are used to determine the coefficient of friction in the Bending Under Tension Test. In general the change in the strip thickness in passing over the die radius is neglected and the radius of curvature to thickness ratio is assumed to be constant in these equations. However, the effect of roller radius, sheet thickness and the surface pressure are also omitted in some of these equations. This work quantitatively determined the effect of roller radius and the tooling pressure on the coefficient of friction. The Bending Under Tension Test was performed using rollers with different radii and also lubricants with different properties. The tool radii were found to have a direct influence in the contact pressure. The effect of roller radius on friction was considerable and it was observed that there is a clear relationship between the contact pressure and the coefficient of friction.

Healthy nature healthy people: 'contact with nature' as an upstream health promotion intervention for populations

Whilst urban-dwelling individuals who seek out parks and gardens appear to intuitively understand the personal health and well-being benefits arising from `contact with nature', public health strategies are yet to maximize the untapped resource nature provides, including the benefits of nature contact as an upstream health promotion intervention for populations. This paper presents a summary of empirical, theoretical and anecdotal evidence drawn from a literature review of the human health benefits of contact with nature. Initial findings indicate that nature plays a vital role in human health and well-being, and that parks and nature reserves play a significant role by providing access to nature for individuals. Implications suggest contact with nature may provide an effective population-wide strategy in prevention of mental ill health, with potential application for sub-populations, communities and individuals at higher risk of ill health. Recommendations include further investigation of `contact with nature' in population health, and examination of the benefits of nature-based interventions. To maximize use of `contact with nature' in the health promotion of populations, collaborative strategies between researchers and primary health, social services, urban planning and environmental management sectors are required. This approach offers not only an augmentation of existing health promotion and prevention activities, but provides the basis for a socio-ecological approach to public health that incorporates environmental sustainability.

Health and well-being naturally: 'contact with nature' in health promotion for targeted individuals, communities and populations

Issue addressed: The increase in mental health disorders worldwide makes it important to recognise health promotion interventions that are effective, accessible and affordable. Although natural spaces are coming to be recognised as health-promoting settings for general populations, little is understood about the use of nature contact in treatment and care for individuals experiencing ill-health.

Methods: This paper provides a summary of key research findings and presents a case study examining the self reported health and well-being benefits of nature contact for a small clinical sample. The 'Spectrum of Interventions for Mental Health Problems and Mental Disorders' provides a conceptual framework for ordering current and future information relating to nature-based interventions.

Results: Evidence demonstrates that separately, physical activity, social connection, and contact with nature enhance human health and well-being. The case example illustrates how 'active', 'social' and 'adventurous' contact with nature may be combined within a treatment intervention to protect and enhance the health of individuals experiencing chronic mental, emotional and physical health difficulties.

Conclusions: 'Contact with nature' constitutes a health promotion strategy with potential application in prevention, early intervention, treatment and care. Recommendations include further research to investigate the benefits of nature contact within existing interventions, and the impacts of 'active' and 'social' nature contact within tailored interventions for targeted individuals and communities.

Children's mental health and wellbeing and hands-on contact with nature

Research on the health and wellbeing benefits of contact with animals and plants indicates the natural environment may have significant positive psychological and physiological effects on human health and wellbeing. In terms of children, studies have demonstrated that children function better cognitively and emotionally in 'green' environments and have more creative play. In Australia as well as internationally, many schools appear to be incorporating nature-based activities into their curricula, mostly via sustainability education. Although these programs appear to be successful, few have been evaluated, particularly in terms of the potential benefits to health and wellbeing. This paper reports on a pilot survey investigating the mental health benefits of contact with nature for primary school children in Melbourne, Australia. A survey of principals and teachers was conducted in urban primary schools within a 20km radius of Melbourne. As well as gathering data on the types and extent of environmental and other nature-based activities in the sample schools, items addressing the perceptions of principals and teachers of the potential effects of these activities on children's mental health and wellbeing were also included. Despite a lower than expected response rate, some interesting findings emerged. Although preliminary, results indicate that participants' perceptions of the benefits to mental health and wellbeing from participation in hands-on nature based activities at their school are positive and encompass many aspects of mental health.

Contact pressure and wear in sheet metal forming - an FEM analysis

Wear is the principal cause of tool failure in most sheet metal forming processes. It is well known that the contact pressure between the blank and the tool has a large influence on the wear of the tool, and hence the tool life. This investigation utilises the finite element method to analyse the contact pressure distribution over the die radius for a particular deep drawing process. Furthermore, the evolution of the predicted contact pressure distribution throughout the entire stroke of the punch is also examined. It was found that the majority of the process shows a steady state pressure distribution, with two characteristic peaks over the die radius, at the beginning and end of the sheet contact area. Interestingly, the initial transient contact pressure response showed extremely high localised peak pressures; more than twice that of the steady state peaks. Results are compared to wear reported in the literature, during similar experimental deep drawing processes. Finally, the significance and effect of the results on wear and wear-testing techniques are discussed.