5,340 research outputs found
Synchronization properties of self-sustained mechanical oscillators
We study, both analytically and numerically, the dynamics of mechanical
oscillators kept in motion by a feedback force, which is generated
electronically from a signal produced by the oscillators themselves. This kind
of self-sustained systems may become standard in the design of
frequency-control devices at microscopic scales. Our analysis is thus focused
on their synchronization properties under the action of external forces, and on
the joint dynamics of two to many coupled oscillators. Existence and stability
of synchronized motion are assessed in terms of the mechanical properties of
individual oscillators --namely, their natural frequencies and damping
coefficients-- and synchronization frequencies are determined. Similarities and
differences with synchronization phenomena in other coupled oscillating systems
are emphasized.Comment: To appear in Phys. Rev.
Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
We address two aspects of the dynamics of the forced Duffing oscillator which
are relevant to the technology of micromechanical devices and, at the same
time, have intrinsic significance to the field of nonlinear oscillating
systems. First, we study the stability of periodic motion when the phase shift
between the external force and the oscillation is controlled -contrary to the
standard case, where the control parameter is the frequency of the force.
Phase-shift control is the operational configuration under which self-sustained
oscillators -and, in particular, micromechanical oscillators- provide a
frequency reference useful for time keeping. We show that, contrary to the
standard forced Duffing oscillator, under phase-shift control oscillations are
stable over the whole resonance curve. Second, we analyze a model for the
internal resonance between the main Duffing oscillation mode and a
higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus
on the stabilization of the oscillation frequency when the resonance takes
place, and present preliminary experimental results that illustrate the
phenomenon. This synchronization process has been proposed to counteract the
undesirable frequency-amplitude interdependence in nonlinear time-keeping
micromechanical devices
Large N reduction on a twisted torus
We consider SU(N) lattice gauge theory at infinite N defined on a torus with
a CP invariant twist. Massless fermions are incorporated in an elegant way,
while keeping them quenched. We present some numerical results which suggest
that twisting can make numerical simulations of planar QCD more efficient.Comment: 14 pages, 2 figures, 1 tabl
Combinatorics of lattice paths with and without spikes
We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.Comment: Latex. 25 page
Large N reduction with overlap fermions
We revisit quenched reduction with fermions and explain how some old problems
can be avoided using the overlap Dirac operator.Comment: Lattice2002(chiral) 3 pages, no figure
Problem Solvers, INC.
Our unit centers on building our students\u27 social-emotional skills. The skills we focus on are listening, following directions, self-control, and problem solving. Using various read-alouds, kid-friendly videos, and visuals, we hope to provide students with tools necessary to become problem-solvers in their daily lives.Students will be introduced to different age-appropriate solutions and practice them in an interactive and fun way. Ideally, this unit should be taught during the first weeks of school in effort to build a positive learning community
Synchronization of a forced self-sustained Duffing oscillator
We study the dynamics of a mechanical oscillator with linear and cubic forces
-the Duffing oscillator- subject to a feedback mechanism that allows the system
to sustain autonomous periodic motion with well-defined amplitude and
frequency. First, we characterize the autonomous motion for both hardening and
softening nonlinearities. Then, we analyze the oscillator's synchronizability
by an external periodic force. We find a regime where, unexpectedly, the
frequency range where synchronized motion is possible becomes wider as the
amplitude of oscillations grows. This effect of nonlinearities may find
application in technological uses of mechanical Duffing oscillators -for
instance, in the design of time-keeping devices at the microscale- which we
briefly review.Comment: To appear in Eur. Phys. J. Special Topic
Two-loop critical mass for Wilson fermions
We have redone a recent two-loop computation of the critical mass for Wilson
fermions in lattice QCD by evaluating Feynman integrals with the
coordinate-space method. We present the results for different types of infrared
regularization. We confirm both the previous numerical estimates and the power
of the coordinate-space method whenever high accuracy is needed.Comment: 13 LaTeX2e pages, 2 ps figures include
La boîte à outils géotechniques de demain: EN 1997-1: 202x Règles générales
This paper describes the development of the final Project Team (PT) draft of the next generation
of Eurocode 7 Part 1 (EN 1997-1:202x). The use of Nationally Determined Parameters and the drive for ease-of-use is highlighted. Key changes from the previous version of EN 1997-1 are explained, including the introduction of the Geotechnical Design Model; revision of the Geotechnical Categories and their application; the implementation of Consequence Classes and Geotechnical Complexity Classes in achieving the reliability required by the Eurocodes; elaboration on the use of numerical methods within Eurocode 7; the treatment of rock on an equal basis with soil; and greater emphasis on the Observational Method.Postprint (published version
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