Changes in the dynamical behavior of nonlinear systems induced by noise.

Weak noise acting upon a nonlinear dynamical system can have far-reaching consequences. The fundamental underlying problem - that of large deviations of a nonlinear system away from a stable or metastable state, sometimes resulting in a transition to a new stationary state, in response to weak additive or multiplicative noise - has long attracted the attention of physicists. This is partly because of its wide applicability, and partly because it bears on the origins of temporal irreversibility in physical processes. During the last few years it has become apparent that, in a system far from thermal equilibrium, even small noise can also result in qualitative change in the system's properties, e.g., the transformation of an unstable equilibrium state into a stable one, and vice versa, the occurrence of multistability and multimodality, the appearance of a mean field, the excitation of noise-induced oscillations, and noise-induced transport (stochastic ratchets). A representative selection of such phenomena is discussed and analyzed, and recent progress made towards their understanding is reviewed

Could You Use That in a Sentence, Please?: The Intersection of Prosecutorial Ethics, Relevant Conduct Sentencing, and Criminal RICO Indictments

This Note highlights a potential prosecutorial abuse at the intersection of RICO and the Sentencing Guidelines; specifically, how a weak RICO charge can create an unfair sentencing advantage over a defendant who is acquitted of that charge but is still convicted of at least one other count. Because this sentencing strategy involves two complex statutory frameworks, this Note requires a detailed overview of both the RICO Act and the current sentencing regime; this is necessary to clearly demonstrate how a faulty RICO indictment can be used to conceptually tie together otherwise unrelated acts and achieve an increased sentence under “relevant conduct” sentencing. Part I will describe the United States Sentencing Guidelines, focusing on the concept of “relevant conduct” sentencing. Part II will discuss the key concepts of RICO, looking closely at the “relatedness” requirement for a RICO “pattern of racketeering activity.” Part III will demonstrate how a prosecutor could use a weak RICO charge and allege a “pattern of racketeering activity” to connect two unrelated acts to one another, in order to argue later that these unrelated acts were part of the “same course of conduct or common scheme” for the purposes of relevant conduct sentencing. This Part will examine the corruption trial of former Alabama Governor Don Siegelman to illustrate how RICO’s “pattern” concept can lead to post-trial confusion when evaluating a defendant’s “common scheme of conduct” at sentencing. Part IV will argue that a prosecutor who intentionally confuses these concepts to gain sentencing leverage behaves both unethically and in a manner contrary to the purposes of the United States Sentencing Guidelines. As a result, this Note will recommend that judges be informed of this problem and that the Department of Justice prohibit this use of RICO indictments as part of its already-established RICO oversight process

Could You Use That in a Sentence, Please?: The Intersection of Prosecutorial Ethics, Relevant Conduct Sentencing, and Criminal RICO Indictments

This Note highlights a potential prosecutorial abuse at the intersection of RICO and the Sentencing Guidelines; specifically, how a weak RICO charge can create an unfair sentencing advantage over a defendant who is acquitted of that charge but is still convicted of at least one other count. Because this sentencing strategy involves two complex statutory frameworks, this Note requires a detailed overview of both the RICO Act and the current sentencing regime; this is necessary to clearly demonstrate how a faulty RICO indictment can be used to conceptually tie together otherwise unrelated acts and achieve an increased sentence under “relevant conduct” sentencing. Part I will describe the United States Sentencing Guidelines, focusing on the concept of “relevant conduct” sentencing. Part II will discuss the key concepts of RICO, looking closely at the “relatedness” requirement for a RICO “pattern of racketeering activity.” Part III will demonstrate how a prosecutor could use a weak RICO charge and allege a “pattern of racketeering activity” to connect two unrelated acts to one another, in order to argue later that these unrelated acts were part of the “same course of conduct or common scheme” for the purposes of relevant conduct sentencing. This Part will examine the corruption trial of former Alabama Governor Don Siegelman to illustrate how RICO’s “pattern” concept can lead to post-trial confusion when evaluating a defendant’s “common scheme of conduct” at sentencing. Part IV will argue that a prosecutor who intentionally confuses these concepts to gain sentencing leverage behaves both unethically and in a manner contrary to the purposes of the United States Sentencing Guidelines. As a result, this Note will recommend that judges be informed of this problem and that the Department of Justice prohibit this use of RICO indictments as part of its already-established RICO oversight process

The not-so-massive black hole in the microquasar GRS1915+105

We present a new dynamical study of the black hole X-ray transient GRS1915+105 making use of near-infrared spectroscopy obtained with X-shooter at the VLT. We detect a large number of donor star absorption features across a wide range of wavelengths spanning the H and K bands. Our 24 epochs covering a baseline of over 1 year permit us to determine a new binary ephemeris including a refined orbital period of P=33.85 +/- 0.16 d. The donor star radial velocity curves deliver a significantly improved determination of the donor semi-amplitude which is both accurate (K_2=126 +/- 1 km/s) and robust against choice of donor star template and spectral features used. We furthermore constrain the donor star's rotational broadening to vsini=21 +/-4 km/s, delivering a binary mass ratio of q=0.042 +/- 0.024. If we combine these new constraints with distance and inclination estimates derived from modelling the radio emission, a black hole mass of M_BH=10.1 +/- 0.6 M_sun is inferred, paired with an evolved mass donor of M_2=0.47 +/- 0.27 M_sun. Our analysis suggests a more typical black hole mass for GRS1915+105 rather than the unusually high values derived in the pioneering dynamical study by Greiner et al. (2001). Our data demonstrate that high-resolution infrared spectroscopy of obscured accreting binaries can deliver dynamical mass determinations with a precision on par with optical studies

Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths

We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology.Comment: 5 pages, 1 figur

Energy-optimal steering of transitions through a fractal basin boundary.

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

Charge fluctuations and boundary conditions of biological ion channels:effect on the ionic transition rate

A self-consistent solution is derived for the Poisson-Nernst-Planck (PNP) equation, valid both inside a biological ion channel and in the adjacent bulk fluid. An iterative procedure is used to match the two solutions together at the channel mouth. Charge fluctuations at the mouth are modeled as shot noise flipping the height of the potential barrier at the selectivity site. The resultant estimates of the conductivity of the ion channel are in good agreement with Gramicidin experimental measurements and they reproduce the observed current saturation with increasing concentration

Mass accretion rate of the galactic black hole A0620-00 in its quiescent state

Our recent radio observation using the Giant Meter Radio Telescope (GMRT) of the galactic black hole transient A0620-00 at 1.280GHz revealed a micro-flare of a few milli-Jansky. Assuming an equipartition of magnetic energy and the gravitational potential energy of accreting matter, it is possible to estimate the upper limit of the accretion rate. Assuming a black hole mass of $10M_\odot$ residing at the center, we find this to be at the most ${\dot M} = (8.5 \pm 1.4) \times 10^{-11} M_\odot$ yr$^{-1}$. This is consistent with earlier estimates of accretion rates based on optical and X-ray observations.Comment: 3 pages 1 figur

Optimal fluctuations and the control of chaos.

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identied with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms