Geometric, Variational Integrators for Computer Animation

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details

Recurrent proofs of the irrationality of certain trigonometric values

We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed

Learning and predicting time series by neural networks

Artificial neural networks which are trained on a time series are supposed to achieve two abilities: firstly to predict the series many time steps ahead and secondly to learn the rule which has produced the series. It is shown that prediction and learning are not necessarily related to each other. Chaotic sequences can be learned but not predicted while quasiperiodic sequences can be well predicted but not learned.Comment: 5 page

A bright nanowire single photon source based on SiV centers in diamond

The practical implementation of many quantum technologies relies on the development of robust and bright single photon sources that operate at room temperature. The negatively charged silicon-vacancy (SiV-) color center in diamond is a possible candidate for such a single photon source. However, due to the high refraction index mismatch to air, color centers in diamond typically exhibit low photon out-coupling. An additional shortcoming is due to the random localization of native defects in the diamond sample. Here we demonstrate deterministic implantation of Si ions with high conversion efficiency to single SiV- centers, targeted to fabricated nanowires. The co-localization of single SiV- centers with the nanostructures yields a ten times higher light coupling efficiency than for single SiV- centers in bulk diamond. This enhanced photon out-coupling, together with the intrinsic scalability of the SiV- creation method, enables a new class of devices for integrated photonics and quantum science.Comment: 15 pages, 5 figure

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Phase-dependent light propagation in atomic vapors

Light propagation in an atomic medium whose coupled electronic levels form a diamond-configuration exhibits a critical dependence on the input conditions. In particular, the relative phase of the input fields gives rise to interference phenomena in the electronic excitation whose interplay with relaxation processes determines the stationary state. We integrate numerically the Maxwell-Bloch equations and observe two metastable behaviors for the relative phase of the propagating fields corresponding to two possible interference phenomena. These phenomena are associated to separate types of response along propagation, minimize dissipation, and are due to atomic coherence. These behaviors could be studied in gases of isotopes of alkali-earth atoms with zero nuclear spin, and offer new perspectives in control techniques in quantum electronics.Comment: 16 pages, 11 figures, v2: typos corrected, v3: final version, to appear in Phys. Rev.

Design aspects related to the reliability of the LHC beam dump kicker systems

The two LHC beam dump kicker systems consist each of 14 pulse generator and magnet subsystems. Their task is to extract on request the beams in synchronisation with the gap in the beam. This operation must be fail-safe to avoid disastrous consequences due to loss of the beam inside the LHC. Only a failing operation of one of the 14 pulse generators is allowed. To preserve this tolerance premature beam dumps are forced immediately after early detection of internal faults. However, these faults should occur rarely in order not to be a source of undesirable downtime of the LHC. The report determines first the level of reliability required for the main components of the system. In particular faults which could cause spontaneously non-synchronised beam dumps are identified. Then, technical solutions are evaluated on failure behaviour. Those having a most likely failure mode which does not cause dump triggers are favoured. These solutions need redundancy and are more complex but have the advantage to be fault tolerant. The design goal can be achieved with a combination of high quality components, redundant signal paths, fault tolerant subsystems, continuous surveillance and check-list validation tests before the start of the injection of beam in the LHC

On the Response of an OST to a Point-like Heat Source

A new technique of superconducting cavity diagnostics has been introduced by D. Hartrill at Cornell University, Ithaca, USA. Oscillating Superleak Transducers (OST) detect the heat transferred from a cavity's quench point via "Second Sound" through the superfluid He bath, needed to cool the superconducting cavity. The observed response of an OST is a complex, but reproducible pattern of oscillations. A small helium evaporation cryostat was built which allows the investigation of the response of an OST in greater detail. The distance between a point-like electrical heater and the OST can be varied. The OST can be mounted either parallel or perpendicular to the plate, housing the heat source. If the artificial quench-point releases an amount of energy compatible to a real quench spot on a cavity's surface, the OST signal starts with a negative pulse, which is usually strong enough to allow automatic detection. Furthermore, the reflection of the Second Sound on the wall is observed. A reflection coefficient R = 0.39 +- 0.05 of the glass wall is measured. This excludes a strong influence of multiple reflections in the complex OST response. Fourier analyses show three main frequencies, found in all OST spectra. They can be interpreted as modes of an oscillating circular membrane.Comment: 10 pages, 16 figure