81 research outputs found
Controlling transitions in a Duffing oscillator by sweeping parameters in time
We consider a high-Q Duffing oscillator in a weakly nonlinear regime with the driving frequency sigma varying in time between sigmai and sigmaf at a characteristic rate r. We found that the frequency sweep can cause controlled transitions between two stable states of the system. Moreover, these transitions are accomplished via a transient that lingers for a long time around the third, unstable fixed point of saddle type. We propose a simple explanation for this phenomenon, and find the transient lifetime to scale as −(ln|r−rc|)/lambdar, where rc is the critical rate necessary to induce a transition and lambdar is the repulsive eigenvalue of the saddle. Experimental implications are mentioned
Stochastic and Collective Properties of Nonlinear Oscillators
Two systems of nonlinear oscillators are considered: (a) a single periodically driven nonlinear oscillator interacting with a heat bath, which may operate in the regime of bistability or monostability, and (b) a one-dimensional chain of self-sustaining phase oscillators with nearest-neighbor interaction.
For a single oscillator we analyze the scaling crossovers in the thermal activation barrier between the two stable states. The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. We establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. Using the instanton method, we map numerically the entire parameter range of bistability and find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then where it would be expected to hold as a result of an overdamped soft mode. Additionally, we uncover a new scaling behavior with exponent of ≈1.3 that extends beyond the close vicinity of the bifurcation point.
We also study the pattern of fluctuational trajectories in the monostable regime. For nonequilibrium systems, fluctuational and relaxational trajectories are not simply related by time-reversibility, as is the case in thermal equilibrium. One of the consequences of this is the onset of singularities in the pattern of fluctuational trajectories, where most probable paths to neighboring states are far away from each other. This also creates nonsmoothness in the probability distribution of the system in its phase space. We discover that the pattern of optimal paths in equilibrium systems is fragile with respect to the driving strength F, and investigate how the singularities occur as the system is driven away from equilibrium. As the strength of the driving F approaches zero, the cusp of the spiral caustic system recedes to larger radius R and the angle of the cusp also decreases. The dependence of R on F displays two scaling laws with crossovers, where the scaling exponents depend on the damping.
For the one-dimensional chain of nearest-neighbor coupled phase oscillators, we develop a renormalization group method to investigate synchronization clusters. We apply it numerically to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies. We find that the distributions of sizes of frequency clusters are exponential, with a characteristic length. The dependence of this length upon parameters of these Lorentzian distributions develops an asymptotic power law with an exponent of 0.48 ± 0.02. The findings obtained with the renormalization group are compared with numerical simulations of the equations of motion of the chain, with an excellent agreement in all the aforementioned quantities.</p
Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers
We report the results of a recent search for the lowest value of thermal
noise that can be achieved in LIGO by changing the shape of mirrors, while
fixing the mirror radius and maintaining a low diffractional loss. The result
of this minimization is a beam with thermal noise a factor of 2.32 (in power)
lower than previously considered Mesa Beams and a factor of 5.45 (in power)
lower than the Gaussian beams employed in the current baseline design. Mirrors
that confine these beams have been found to be roughly conical in shape, with
an average slope approximately equal to the mirror radius divided by arm
length, and with mild corrections varying at the Fresnel scale. Such a mirror
system, if built, would impact the sensitivity of LIGO, increasing the event
rate of observing gravitational waves in the frequency range of maximum
sensitivity roughly by a factor of three compared to an Advanced LIGO using
Mesa beams (assuming all other noises remain unchanged). We discuss the
resulting beam and mirror properties and study requirements on mirror tilt,
displacement and figure error, in order for this beam to be used in LIGO
detectors.Comment: 9 pages, 11 figure
Gauge Dressing of 2D Field Theories
By using the gauge Ward identities, we study correlation functions of gauged
WZNW models. We show that the gauge dressing of the correlation functions can
be taken into account as a solution of the Knizhnik-Zamolodchikov equation. Our
method is analogous to the analysis of the gravitational dressing of 2D field
theories.Comment: 13 pages, Late
Hierarchy of protein loop-lock structures: a new server for the decomposition of a protein structure into a set of closed loops
HoPLLS (Hierarchy of protein loop-lock structures)
(http://leah.haifa.ac.il/~skogan/Apache/mydata1/main.html) is a web server that
identifies closed loops - a structural basis for protein domain hierarchy. The
server is based on the loop-and-lock theory for structural organisation of
natural proteins. We describe this web server, the algorithms for the
decomposition of a 3D protein into loops and the results of scientific
investigations into a structural "alphabet" of loops and locks.Comment: 11 pages, 4 figure
- …