Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Mastectomy, Body De-Construction and Impact on Identity: A qualitative study

Objectives: This qualitative study aims at understanding the consequences of body deconstruction through mastectomy on corporality and identity in women with breast cancer. Design: Nineteen women were contacted through the hospital. All had to undergo mastectomy. Some were offered immediate breast reconstruction, others, because of cancer treatments, had no planned reconstruction. A qualitative reflexive methodological background was chosen. Method: Women were invited to participate in three semi-structured interviews, one shortly before or after mastectomy, and the other interviews later in their illness courses, after surgery. All interviews were transcribed verbatim. Thematic analysis was performed. The analysis of the first interview of each woman is presented in this article. Results: Mastectomy provokes a painful experience of body deconstruction. Even when immediate reconstruction is proposed, contrasted feelings and dissonance are expressed when comparing the former healthy body to the present challenged body entity. Body transformations are accompanied with experiences of mutilation, strangeness, and modify the physical, emotional social, symbolic and relational dimensions of the woman's gendered identity. Although the opportunity of breast reconstruction is seen as a possible recovery of a lost physical symmetry and body integrity, grieving the past body and integrating a new corporality leads to a painful identity crisis. Conclusion: With mastectomy, the roots of the woman's identity are challenged, leading to a re-evaluation of her existential values. The consequences of mastectomy transform the woman's corporality and embodiment, and question her identity. Psychological support is discussed in the perspective of our results.

Percolation and three-dimensional structure of supercritical water

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompa- nied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Fluctuation relation for weakly ergodic aging systems

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed

Effects of 2 different prior endurance exercises on whole-body fat oxidation kinetics: light vs. heavy exercise.

This study aimed to compare the effects of 2 different prior endurance exercises on subsequent whole-body fat oxidation kinetics. Fifteen men performed 2 identical submaximal incremental tests (Incr2) on a cycle ergometer after (i) a ∼40-min submaximal incremental test (Incr1) followed by a 90-min continuous exercise performed at 50% of maximal aerobic power-output and a 1-h rest period (Heavy); and (ii) Incr1 followed by a 2.5-h rest period (Light). Fat oxidation was measured using indirect calorimetry and plotted as a function of exercise intensity during Incr1 and Incr2. A sinusoidal equation, including 3 independent variables (dilatation, symmetry and translation), was used to characterize the fat oxidation kinetics and to determine the intensity (Fat(max)) that elicited the maximal fat oxidation (MFO) during Incr. After the Heavy and Light trials, Fat(max), MFO, and fat oxidation rates were significantly greater during Incr2 than Incr1 (p < 0.001). However, Δ (i.e., Incr2-Incr1) Fat(max), MFO, and fat oxidation rates were greater in the Heavy compared with the Light trial (p < 0.05). The fat oxidation kinetics during Incr2(Heavy) showed a greater dilatation and rightward asymmetry than Incr1(Heavy), whereas only a greater dilatation was observed in Incr2(Light) (p < 0.05). This study showed that although to a lesser extent in the Light trial, both prior exercise sessions led to an increase in Fat(max), MFO, and absolute fat oxidation rates during Incr2, inducing significant changes in the shape of the fat oxidation kinetics.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Large D gravity and low D strings

We show that in the limit of a large number of dimensions a wide class of nonextremal neutral black holes has a universal near-horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains the properties of massless scalars found recently in the large-D limit. For black branes with string charges, the near-horizon geometry is that of the three-dimensional black strings of Horne and Horowitz. The analogies between the α′ expansion in string theory and the large-D expansion in gravity suggest a possible effective string description of the large-D limit of black holes. We comment on applications to several subjects, in particular to the problem of critical collapse.

Characterization of phosphate structures in biochar from swine bones

The objective of this work was to develop an alternative methodology to study and characterize the phosphate crystalline properties, directly associated with solubility and plant availability, in biochar from swine bones. Some phosphate symmetry properties of pyrolyzed swine bones were established, using solid state nuclear magnetic resonance spectroscopy, principal component analysis, and multivariate curve resolution analysis, on four pyrolyzed samples at different carbonization intensities. Increasing carbonization parameters (temperature or residence time) generates diverse phosphate structures, increasing their symmetry and decreasing the crossed polarizability of the pair ¹H-31P, producing phosphates with, probably, lower solubility than the ones produced at lower carbonization intensity. Additionally, a new methodology is being developed to study and characterize phosphate crystalline properties directly associated with phosphate solubility and availability to plants.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available