2,407 research outputs found
Time delay in the Kuramoto model with bimodal frequency distribution
We investigate the effects of a time-delayed all-to-all coupling scheme in a
large population of oscillators with natural frequencies following a bimodal
distribution. The regions of parameter space corresponding to synchronized and
incoherent solutions are obtained both numerically and analytically for
particular frequency distributions. In particular we find that bimodality
introduces a new time scale that results in a quasiperiodic disposition of the
regions of incoherence.Comment: 5 pages, 4 figure
Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron
The observation of hysteresis effects in single molecule magnets like
Mn-acetate has initiated ideas of future applications in storage
technology. The appearance of a hysteresis loop in such compounds is an outcome
of their magnetic anisotropy. In this Letter we report that magnetic hysteresis
occurs in a spin system without any anisotropy, specifically, where spins
mounted on the vertices of an icosahedron are coupled by antiferromagnetic
isotropic nearest-neighbor Heisenberg interaction giving rise to geometric
frustration. At T=0 this system undergoes a first order metamagnetic phase
transition at a critical field \Bcrit between two distinct families of ground
state configurations. The metastable phase of the system is characterized by a
temperature and field dependent survival probability distribution.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Vacuum solutions which cannot be written in diagonal form
A vacuum solution of the Einstein gravitational field equation is given that
follows from a general ansatz but fails to follow from it if a certain
symmetric matrix is assumed to be in diagonal form from the beginning.Comment: 18 pages, latex, no figures. An Acknowledgement, 4 references, and
the section "Note added" are adde
Developing a Complex Independent Component Analysis (CICA) technique to extract non-stationary patterns from geophysical time series
In recent decades, decomposition techniques have enabled increasingly more applications for dimension reduction, as well as extraction of additional information from geophysical time series. Traditionally, the principal component analysis (PCA)/empirical orthogonal function (EOF) method and more recently the independent component analysis (ICA) have been applied to extract, statistical orthogonal (uncorrelated), and independent modes that represent the maximum variance of time series, respectively. PCA and ICA can be classified as stationary signal decomposition techniques since they are based on decomposing the autocovariance matrix and diagonalizing higher (than two) order statistical tensors from centered time series, respectively. However, the stationarity assumption in these techniques is not justified for many geophysical and climate variables even after removing cyclic components, e.g., the commonly removed dominant seasonal cycles. In this paper, we present a novel decomposition method, the complex independent component analysis (CICA), which can be applied to extract non-stationary (changing in space and time) patterns from geophysical time series. Here, CICA is derived as an extension of real-valued ICA, where (a) we first define a new complex dataset that contains the observed time series in its real part, and their Hilbert transformed series as its imaginary part, (b) an ICA algorithm based on diagonalization of fourth-order cumulants is then applied to decompose the new complex dataset in (a), and finally, (c) the dominant independent complex modes are extracted and used to represent the dominant space and time amplitudes and associated phase propagation patterns. The performance of CICA is examined by analyzing synthetic data constructed from multiple physically meaningful modes in a simulation framework, with known truth. Next, global terrestrial water storage (TWS) data from the Gravity Recovery And Climate Experiment (GRACE) gravimetry mission (2003–2016), and satellite radiometric sea surface temperature (SST) data (1982–2016) over the Atlantic and Pacific Oceans are used with the aim of demonstrating signal separations of the North Atlantic Oscillation (NAO) from the Atlantic Multi-decadal Oscillation (AMO), and the El Niño Southern Oscillation (ENSO) from the Pacific Decadal Oscillation (PDO). CICA results indicate that ENSO-related patterns can be extracted from the Gravity Recovery And Climate Experiment Terrestrial Water Storage (GRACE TWS) with an accuracy of 0.5–1 cm in terms of equivalent water height (EWH). The magnitude of errors in extracting NAO or AMO from SST data using the complex EOF (CEOF) approach reaches up to ~50% of the signal itself, while it is reduced to ~16% when applying CICA. Larger errors with magnitudes of ~100% and ~30% of the signal itself are found while separating ENSO from PDO using CEOF and CICA, respectively. We thus conclude that the CICA is more effective than CEOF in separating non-stationary patterns
Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion
We provide exact analytical expressions for the magnetic susceptibility
function in the high temperature expansion for finite Heisenberg spin systems
with an arbitrary coupling matrix, arbitrary single-spin quantum number, and
arbitrary number of spins. The results can be used to determine unknown
exchange parameters from zero-field magnetic susceptibility measurements
without diagonalizing the system Hamiltonian. We demonstrate the possibility of
reconstructing the exchange parameters from simulated data for two specific
model systems. We examine the accuracy and stability of the proposed method.Comment: 13 pages, 7 figures, submitted to Phys. Rev.
Spin systems with dimerized ground states
In view of the numerous examples in the literature it is attempted to outline
a theory of Heisenberg spin systems possessing dimerized ground states (``DGS
systems") which comprises all known examples. Whereas classical DGS systems can
be completely characterized, it was only possible to provide necessary or
sufficient conditions for the quantum case. First, for all DGS systems the
interaction between the dimers must be balanced in a certain sense. Moreover,
one can identify four special classes of DGS systems: (i) Uniform pyramids,
(ii) systems close to isolated dimer systems, (iii) classical DGS systems, and
(iv), in the case of , systems of two dimers satisfying four
inequalities. Geometrically, the set of all DGS systems may be visualized as a
convex cone in the linear space of all exchange constants. Hence one can
generate new examples of DGS systems by positive linear combinations of
examples from the above four classes.Comment: With corrections of proposition 4 and other minor change
The tetralogy of Birkhoff theorems
We classify the existent Birkhoff-type theorems into four classes: First, in
field theory, the theorem states the absence of helicity 0- and spin 0-parts of
the gravitational field. Second, in relativistic astrophysics, it is the
statement that the gravitational far-field of a spherically symmetric star
carries, apart from its mass, no information about the star; therefore, a
radially oscillating star has a static gravitational far-field. Third, in
mathematical physics, Birkhoff's theorem reads: up to singular exceptions of
measure zero, the spherically symmetric solutions of Einstein's vacuum field
equation with Lambda = 0 can be expressed by the Schwarzschild metric; for
Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in
differential geometry, any statement of the type: every member of a family of
pseudo-Riemannian space-times has more isometries than expected from the
original metric ansatz, carries the name Birkhoff-type theorem. Within the
fourth of these classes we present some new results with further values of
dimension and signature of the related spaces; including them are some
counterexamples: families of space-times where no Birkhoff-type theorem is
valid. These counterexamples further confirm the conjecture, that the
Birkhoff-type theorems have their origin in the property, that the two
eigenvalues of the Ricci tensor of two-dimensional pseudo-Riemannian spaces
always coincide, a property not having an analogy in higher dimensions. Hence,
Birkhoff-type theorems exist only for those physical situations which are
reducible to two dimensions.Comment: 26 pages, updated references, minor text changes, accepted by Gen.
Relat. Gra
Functional domains in the bacteriophage ø29 terminal protein for interaction with the ø29 DNA polymerase and with DNA
Deletion mutants at the amino- and carboxyl-ends of the ø29 terminal protein, as well as internal deletion and substitution mutants, whose ability to prime the initiation of ø29 DNA replication was affected to different extent, have been assayed for their capacity to interact with DNA or with the ø29 DNA polymerase. One DNA binding domain at the amino end of the terminal protein has been mapped. Two regions involved in the binding to the DNA polymerase, an internal region near the amino-terminus and a carboxyl-terminal one, have been also identified. Interaction with both DNA and ø29 DNA polymerase are required to led to the formation of terminal protein-dAMP initiation complex to start ø29 DNA replication.Peer reviewe
Continuous families of isospectral Heisenberg spin systems and the limits of inference from measurements
We investigate classes of quantum Heisenberg spin systems which have
different coupling constants but the same energy spectrum and hence the same
thermodynamical properties. To this end we define various types of
isospectrality and establish conditions for their occurence. The triangle and
the tetrahedron whose vertices are occupied by spins 1/2 are investigated in
some detail. The problem is also of practical interest since isospectrality
presents an obstacle to the experimental determination of the coupling
constants of small interacting spin systems such as magnetic molecules
Two-dimensional higher-derivative gravity and conformal transformations
We consider the lagrangian in classical (=non-quantized)
two-dimensional fourth-order gravity and give new relations to Einstein's
theory with a non-minimally coupled scalar field. We distinguish between
scale-invariant lagrangians and scale-invariant field equations. is
scale-invariant for F = c_1 R\sp {k+1} and a divergence for . The
field equation is scale-invariant not only for the sum of them, but also for
. We prove this to be the only exception and show in which sense it
is the limit of \frac{1}{k} R\sp{k+1} as . More generally: Let be
a divergence and a scale-invariant lagrangian, then has a
scale-invariant field equation. Further, we comment on the known generalized
Birkhoff theorem and exact solutions including black holes.Comment: 16 pages, latex, no figures, [email protected], Class. Quant.
Grav. to appea
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