6,658 research outputs found
Adjoints and Low-rank Covariance Representation
Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system
Ground states and formal duality relations in the Gaussian core model
We study dimensional trends in ground states for soft-matter systems.
Specifically, using a high-dimensional version of Parrinello-Rahman dynamics,
we investigate the behavior of the Gaussian core model in up to eight
dimensions. The results include unexpected geometric structures, with
surprising anisotropy as well as formal duality relations. These duality
relations suggest that the Gaussian core model possesses unexplored symmetries,
and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org
Low-dimensional Representation of Error Covariance
Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix
Polaron Transport in the Paramagnetic Phase of Electron-Doped Manganites
The electrical resistivity, Hall coefficient, and thermopower as functions of
temperature are reported for lightly electron-doped Ca(1-x)La(x)MnO(3)(0 <= x
<= 0.10). Unlike the case of hole-doped ferromagnetic manganites, the magnitude
and temperature dependence of the Hall mobility for these compounds is found to
be inconsistent with small-polaron theory. The transport data are better
described by the Feynman polaron theory and imply intermediate coupling (alpha
\~ 5.4) with a band effective mass, m*~4.3 m_0, and a polaron mass, m_p ~ 10
m_0.Comment: 7 pp., 7 Fig.s, to be published, PR
Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition
We use a self-assembled two-dimensional Coulomb crystal of ions in
the presence of an external transverse field to engineer a simulator of the
Dicke Hamiltonian, an iconic model in quantum optics which features a quantum
phase transition between a superradiant/ferromagnetic and a normal/paramagnetic
phase. We experimentally implement slow quenches across the quantum critical
point and benchmark the dynamics and the performance of the simulator through
extensive theory-experiment comparisons which show excellent agreement. The
implementation of the Dicke model in fully controllable trapped ion arrays can
open a path for the generation of highly entangled states useful for enhanced
metrology and the observation of scrambling and quantum chaos in a many-body
system.Comment: 6 + 5 pages, 2 + 5 figures. arXiv admin note: substantial text
overlap with arXiv:1711.0739
Conditioning of the Stable, Discrete-time Lyapunov Operator
The Schatten p-norm condition of the discrete-time Lyapunov operator L(sub A) defined on matrices P is identical with R(sup n X n) by L(sub A) P is identical with P - APA(sup T) is studied for stable matrices A is a member of R(sup n X n). Bounds are obtained for the norm of L(sub A) and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov equation (DALE) L(sub A)P = Q can be ill-conditioned only when either L(sub A) or Q is ill-conditioned, these bounds are useful in determining whether P admits a low-rank approximation, which is important in the numerical solution of the DALE for large n
Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution
We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case
Doping Dependence of Polaron Hopping Energies in La(1-x)Ca(x)MnO(3) (0<= x<= 0.15)
Measurements of the low-frequency (f<= 100 kHz) permittivity at T<= 160 K and
dc resistivity (T<= 430 K) are reported for La(1-x)Ca(x)MnO(3) (0<= x<= 0.15).
Static dielectric constants are determined from the low-T limiting behavior of
the permittivity. The estimated polarizability for bound holes ~ 10^{-22}
cm^{-3} implies a radius comparable to the interatomic spacing, consistent with
the small polaron picture established from prior transport studies near room
temperature and above on nearby compositions. Relaxation peaks in the
dielectric loss associated with charge-carrier hopping yield activation
energies in good agreement with low-T hopping energies determined from
variable-range hopping fits of the dc resistivity. The doping dependence of
these energies suggests that the orthorhombic, canted antiferromagnetic ground
state tends toward an insulator-metal transition that is not realized due to
the formation of the ferromagnetic insulating state near Mn(4+) concentration ~
0.13.Comment: PRB in press, 5 pages, 6 figure
Impact of a Resident-Guided Rounding Initiative on the Hospital Consumer Assessment of Healthcare Providers and Systems Survey Scores in Orthopaedic Surgery Inpatients.
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