1,877 research outputs found
Functional control of network dynamics using designed Laplacian spectra
Complex real-world phenomena across a wide range of scales, from aviation and
internet traffic to signal propagation in electronic and gene regulatory
circuits, can be efficiently described through dynamic network models. In many
such systems, the spectrum of the underlying graph Laplacian plays a key role
in controlling the matter or information flow. Spectral graph theory has
traditionally prioritized unweighted networks. Here, we introduce a
complementary framework, providing a mathematically rigorous weighted graph
construction that exactly realizes any desired spectrum. We illustrate the
broad applicability of this approach by showing how designer spectra can be
used to control the dynamics of various archetypal physical systems.
Specifically, we demonstrate that a strategically placed gap induces chimera
states in Kuramoto-type oscillator networks, completely suppresses pattern
formation in a generic Swift-Hohenberg model, and leads to persistent
localization in a discrete Gross-Pitaevskii quantum network. Our approach can
be generalized to design continuous band gaps through periodic extensions of
finite networks.Comment: 9 pages, 5 figure
Reversible signal transmission in an active mechanical metamaterial
Mechanical metamaterials are designed to enable unique functionalities, but
are typically limited by an initial energy state and require an independent
energy input to function repeatedly. Our study introduces a theoretical active
mechanical metamaterial that incorporates a biological reaction mechanism to
overcome this key limitation of passive metamaterials. Our material allows for
reversible mechanical signal transmission, where energy is reintroduced by the
biologically motivated reaction mechanism. By analysing a coarse grained
continuous analogue of the discrete model, we find that signals can be
propagated through the material by a travelling wave. Analysis of the continuum
model provides the region of the parameter space that allows signal
transmission, and reveals similarities with the well-known FitzHugh-Nagumo
system. We also find explicit formulae that approximate the effect of the
timescale of the reaction mechanism on the signal transmission speed, which is
essential for controlling the material.Comment: 20 pages, 7 figure
The geometry of dual isomonodromic deformations
The JMMS equations are studied using the geometry of the spectral curve of a
pair of dual systems. It is shown that the equations can be represented as
time-independent Hamiltonian flows on a Jacobian bundle
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Motion of the cello bridge
This paper presents an experimental investigation of the motion of the bridge of a cello, in the frequency range up to 2 kHz. Vibration measurements were carried out on three different cellos, and the results used to determine the position of the Instantaneous Centre of rotation of the bridge, treated as a rigid body. The assumption of rigid body rotation is shown to give a good approximation up to at least 1 kHz. The instantaneous centre moves from the sound-post side of the bridge at the lowest frequencies towards the bass-bar side at higher frequencies, remaining close to the surface of the top plate of the instrument. The trajectory as a function of frequency sheds light on the response of the cello in response to excitation by bowing the different strings. The correlation between the motion at the four string notches and directly measured transfer functions at these four notches is examined and verified for some important low-frequency body resonances.This work was supported by National Natural Science Foundation of China (NSFC) Grant No. 11504246
A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust
In the present work, we study the quantum cosmology description of closed
Friedmann-Robertson-Walker models in the presence of a positive cosmological
constant and a generic perfect fluid. We work in the Schutz's variational
formalism. If one uses the scale factor and its canonically conjugated momentum
as the phase space variables that describe the geometrical sector of these
models, one obtains Wheeler-DeWitt equations with operator ordering
ambiguities. In order to avoid those ambiguities and simplify the quantum
treatment of the models, we introduce new phase space variables. We explicitly
demonstrate that the transformation leading from the old set of variables to
the new one is canonical. In order to show that the above canonical
transformations simplify the quantum treatment of those models, we consider a
particular model where the perfect fluid is dust. We solve the Wheeler-DeWitt
equation numerically using the Crank-Nicholson scheme and determine the time
evolution of the initial wave function. Finally, we compare the results for the
present model with the ones for another model where the only difference is the
presence of a radiative perfect fluid, instead of dust.Comment: Revtex4, 18 pages, 2 EPS figure
The Landau electron problem on a cylinder
We consider the quantum mechanics of an electron confined to move on an
infinite cylinder in the presence of a uniform radial magnetic field. This
problem is in certain ways very similar to the corresponding problem on the
infinite plane. Unlike the plane however, the group of symmetries of the
magnetic field, namely, rotations about the axis and the axial translations, is
{\em not} realized by the quantum electron but only a subgroup comprising
rotations and discrete translations along the axial direction, is. The basic
step size of discrete translations is such that the flux through the `unit
cylinder cell' is quantized in units of the flux quantum. The result is derived
in two different ways: using the condition of projective realization of
symmetry groups and using the more familiar approach of determining the
symmetries of a given Hamiltonian.Comment: 26 pages, revtex file, no figures. In version 2, introduction is
expanded to explain our approach and references are updated. Results and
conclusions are unchange
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