Abstract:
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. We apply the technique in the of study two and three self-gravitating particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and noted differences in the structural stability, e.g., binary systems were found only in the general relativistic approach.

Abstract:
The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test particles. For the prolate quadrupolar deformations we found chaotic motions contrary to the oblate case where only regular motion is found. We also study the metric that represents a rotating black hole deformed by a quadrupolar term. This metric is obtained as a two soliton solution in the context of Belinsky--Zakharov inverse scattering method. The stability of geodesics depends strongly on the relative direction of the spin of the center of attraction and the test particle angular momentum. The rotation does not alter the regularity of geodesic motions in the oblate case, i.e., the orbits in this case remain regular. We also employ the method of Lyapounov characteristic numbers to examine the stability of orbits evolving around deformed nonrotating centers of attraction. The typical time to observe instability of orbits is analyzed.

Abstract:
The motion of particles in the field of forces associated to an axially symmetric attraction center modeled by a monopolar term plus a prolate quadrupole deformation is studied using Poincare surface of sections and Lyapunov characteristic numbers. We find chaotic motion for certain values of the parameters, and that the instability of the orbits increases when the quadrupole parameter increases. A general relativistic analogue is briefly discussed.

Abstract:
The Newtonian as well as the special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole plus a dipolar halo. The black hole is modeled by either the usual monopole potential or the Paczynki-Wiita pseudo-Newtonian potential. The full general relativistic similar case is also considered. The Poincare section method and the Lyapunov characteristic exponents show that the orbits for the pseudo-Newtonian potential models are more unstable than the corresponding general relativistic geodesics.

j-lanes hashing is a tree mode that splits an input message to j slices, computes j independent digests of each slice, and outputs the hash value of their concatenation. We demonstrate the performance advantage of j-lanes hashing on SIMD architectures, by coding a 4-lanes-SHA-256 implementation and measuring its performance on the latest 3^{rd} Generation Intel^{R} Core^{TM}. For messages whose lengths range from 2KB to 132KB, we show that the 4-lanes SHA-256 is between 1.5 to 1.97 times faster than the fastest publicly available implementation that we are aware of, and between ~2 to ~2.5 times faster than the OpenSSL 1.0.1c implementation. For long messages, there is no significant performance difference between different choices of j. We show that the 4-lanes SHA-256 is faster than the two SHA3 finalists (BLAKE and Keccak) that have a published tree mode implementation. Finally, we explain why j-lanes hashing will be faster on the coming AVX2 architecture that facilitates using 256 bits registers. These results suggest that standardizing a tree mode for hash functions (SHA-256 in particular) could be useful for performance hungry applications.

j-lanes tree hashing is a tree mode
that splits an input message intojslices, computesjindependent digests of each slice, and
outputs the hash value of their concatenation.j-pointers tree hashing is a
similar tree mode that receives, as input,jpointers tojmessages (or slices of a single message),
computes their digests and outputs the hash value of their concatenation. Such
modes expose parallelization opportunities in a hashing process that is
otherwise serial by nature. As a result, they have a performance advantage on
modern processor architectures. This paper provides precise specifications for
these hashing modes, proposes appropriate IVs, and demonstrates their
performance on the latest processors. Our hope is that it would be useful for standardization
of these modes.

Abstract:
We describe a method for efficiently hashing multiple messages of different lengths. Such computations occur in various scenarios, and one of them is when an operating system checks the integrity of its components during boot time. These tasks can gain performance by parallelizing the computations and using SIMD architectures. For such scenarios, we compare the performance of a new 4-buffers SHA-256 S-HASH implementation, to that of the standard serial hashing. Our results are measured on the 2nd Generation Intel^{?} Core^{TM} Processor, and demonstrate SHA-256 processing at effectively ~5.2 Cycles per Byte, when hashing from any of the three cache levels, or from the system memory. This represents speedup by a factor of 3.42x compared to OpenSSL (1.0.1), and by 2.25x compared to the recent and faster n-SMS method. For hashing from a disk, we show an effective rate of ~6.73 Cycles/Byte, which is almost 3 times faster than OpenSSL (1.0.1) under the same conditions. These results indicate that for some usage models, SHA-256 is significantly faster than commonly perceived.

Abstract:
Wisdom has recently unveiled a new relativistic effect, called ``spacetime swimming'', where quasi-rigid free bodies in curved spacetimes can "speed up", "slow down" or "deviate" their falls by performing "local" cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a non-relativistic related one, named here ``space swinging'', where the fall is altered through "nonlocal" cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large red-shift regions.

Abstract:
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the third body is a test-particle. We focus on the orbits around the 3:2 resonance. We show that, in spite of the notable difference between the relativistic and Newtonian orbits, most of the resonant region is preserved. Nevertheless, differently from the Newtonian case, the frequencies between the second and the third body are no longer commensurable.

Abstract:
We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero resistance state at low temperature, zero magnetic field, and high doping. We find a striking suppression of the critical current near graphene\rq{}s charge neutrality point, which we attribute to specular reflexion of Andreev pairs at the interface of charge puddles. This type of reflexion, specific to the Dirac band structure, had up to now remained elusive. At high magnetic field the use of superconducting electrodes with high critical field enables the investigation of the proximity effect in the Quantum Hall regime. Although the supercurrent is not directly detectable in our two wire configuration, interference effects are visible which may be attributed to the injection of Cooper pairs into edge states.