Mechanisms for the Development of Locally Low-Dimensional Atmospheric Dynamics

2005 ◽  
Vol 62 (4) ◽  
pp. 1135-1156 ◽  
Author(s):  
Michael Oczkowski ◽  
Istvan Szunyogh ◽  
D. J. Patil
Keyword(s):  
Phase Space ◽  
Numerical Experiments ◽  
Practical Implication ◽  
Finite Amplitude ◽  
Diagnostic Tools ◽  
Atmospheric Flow ◽  
Initial Transient ◽  
Wide Range ◽  
Environmental Prediction ◽  
Low Dimensional

Abstract The complexity of atmospheric instabilities is investigated by a combination of numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well-established analysis of the local energetics of the atmospheric flow and the recently introduced ensemble dimension (E dimension). The E dimension is a local measure that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions over a geographically localized region. The E dimension is maximal, that is, equal to the number of ensemble members (k), when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E dimension. Numerical experiments with the state-of-the-art operational Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) at a reduced resolution are carried out to investigate the spatiotemporal evolution of the E dimension. This evolution is characterized by an initial transient phase in which coherent regions of low dimensionality develop through a rapid local decay of the E dimension. The typical duration of the transient is between 12 and 48 h depending on the flow; after the initial transient, the E dimension gradually increases with time. The main goal of this study is to identify processes that contribute to transient local low-dimensional behavior. Case studies are presented to show that local baroclinic and barotropic instabilities, downstream development of upper-tropospheric wave packets, phase shifts of finite amplitude waves, anticyclonic wave breaking, and some combinations of these processes can all play crucial roles in lowering the E dimension. The practical implication of the results is that a wide range of synoptic-scale weather events may exist whose prediction can be significantly improved in the short and early medium range by enhancing the prediction of only a few local phase space directions. This potential is demonstrated by a reexamination of the targeted weather observations missions from the 2000 Winter Storm Reconnaissance (WSR00) program.

scholarly journals Slug genesis in cylindrical pipe flow

2010 ◽  
Vol 663 ◽  
pp. 180-208 ◽  
Author(s):  
Y. DUGUET ◽  
A. P. WILLIS ◽  
R. R. KERSWELL
Keyword(s):  
Phase Space ◽  
Vortex Shedding ◽  
Coherent Structures ◽  
Pipe Flow ◽  
Edge State ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Spatial Expansion ◽  
Cylindrical Pipe ◽  
Low Dimensional

Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called ‘slugs’, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a ‘slug’. This entails first identifying the relative attractor – ‘edge state’ – on the laminar–turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at Re ≈ 2300, the edge state is found to be localized over the range Re = 2000–6000, and progressively reduces in both energy and spatial extent as Re is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin–Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state's upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues

2021 ◽  
Author(s):  
Sven-Erik Ekström ◽  
Paris Vassalos
Keyword(s):  
Distribution Function ◽  
Asymptotic Distribution ◽  
Numerical Experiments ◽  
Toeplitz Matrices ◽  
Future Research ◽  
Research Directions ◽  
Numerical Examples ◽  
Working Hypothesis ◽  
Wide Range ◽  
Future Research Directions

AbstractIt is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$ f , appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$ f is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$ f . The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$ f is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$ f . Future research directions are outlined at the end of the paper.

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

2008 ◽  
Vol 38 (6) ◽  
pp. 1145-1165 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari ◽  
Robert Hallberg
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Climate Impacts ◽  
Surface Mixed Layer ◽  
Rotation Rates ◽  
Wide Range ◽  
Horizontal Density Gradient ◽  
Mixed Layers

Abstract Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

scholarly journals Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1498
Author(s):  
Karel J. in’t Hout ◽  
Jacob Snoeijer
Keyword(s):  
Principal Component Analysis ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Principal Component ◽  
Partial Differential ◽  
Basket Options ◽  
Basket Option ◽  
Option Values ◽  
Convergence Behaviour ◽  
Low Dimensional

We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals Comparative Study of Immune-Diagnostic Tools with Polymerase Chain Reaction in Sub-Clinical Leishmaniasis Isolates

2011 ◽  
Vol 12 (1) ◽  
pp. 34-39 ◽  
Author(s):  
Nazar M Abdalla
Keyword(s):  
Polymerase Chain Reaction ◽  
Skin Test ◽  
Diagnostic Methods ◽  
Diagnostic Tools ◽  
Enzyme Linked Immunosorbent Assay ◽  
Clinical Form ◽  
Chain Reaction ◽  
Leishmanin Skin Test ◽  
Wide Range ◽  
Polymerase Chain

Objective: This study aimed to identify cases of leishmaniasis in the Nuba Mountain area, which is situated in a unique geographical site located in the centre of Sudanese leishmania belt. Wide range of investigations are available for detection of leishmania cases, but still the most reliable and easy test used as screening and epidemiological tool in field studies needs to be evaluated. The most commonly used conventional diagnostic methods direct microscopy and culture have some drawbacks in diagnosing subclinical cases of leishmaniasis. Materials and methods: In this study, comparative properties of various immune-diagnostic tools with Polymerase Chain Reaction used in sub-clinical leishmaniasis isolates were explored. The immune-diagnostic tools involved in this study include- Leishmanin Skin Test (LST), Enzyme Linked Immunosorbent Assay (ELISA) and Direct Agglutination Test (DAT). The study was conducted in the Green Valley village (Rashad Province, South Kordofan State) with a population of 332. Most of the villagers presented with sub-clinical form of leishmaniasis with minor symptoms and signs without the features found in clinical form of visceral leishmaniasis such as fever, diarrhoea, epistaxis, enlarged lymph nodes, spleen and liver. In this study we collected demographic, clinical and epidemiological data using special questionnaire. Leishmanin skin test (LST), ELISA, DAT and PCR for parasite DNA detection were used. Result: The final positive cases detected by PCR were 32 out of 332 belong to L. donovani species. The final positive cases detected by LST were 51.2% of the total population under study, while 11 out of the 37 tested samples were positive by ELISA. All of the 332 villagers showed negative readings by DAT with exception of three individuals who were positive with very high titers. Conclusion: DNA etxtraction and amplification with primers can be a good screening tool in subclinical leishmaniasis isolates. Keyword: Sub-clinical; Leishmaniasis; Leishmanin Skin Test; ELISA; DAT; PCR. DOI: 10.3329/jom.v12i1.5422J Medicine 2011; 12 : 34-39

scholarly journals Difficulties in the differential diagnosis of tumors in the female reproductive system

2020 ◽  
Vol 13 (4) ◽  
pp. 369-383
Author(s):  
Ju. V. Nosova ◽  
A. E. Solopova ◽  
G. N. Khabas ◽  
A. V. Asaturova
Keyword(s):  
Differential Diagnosis ◽  
Inflammatory Reaction ◽  
Wilms Tumor ◽  
Imaging Techniques ◽  
Uterine Cancer ◽  
Diagnostic Errors ◽  
Diagnostic Tools ◽  
Cytokeratin 20 ◽  
Pelvic Tumors ◽  
Wide Range

Introduction. Most pelvic tumors originate from reproductive organs. Even using the up-to-date imaging techniques, radiologists experience difficulties in determining the source of the lesion since a wide range of tumors look similar to each other on the distorted backdrop of pelvic anatomy, large invasive formations, and an active inflammatory reaction of the pelvic peritoneum.Aim: to evaluate “pitfalls” in the preoperative noninvasive diagnosis of female pelvic tumors by applying the clinical diagnostic tools.Materials and methods. Four rare clinical cases were analyzed; all of them posed difficulties in interpreting the diagnostic examination due to their atypical characteristics. There were 2 cases of ovarian cancer, initially identified by an experienced team of radiologists as benign pelvic pathology. Also, there were fibroids with degeneration, marked proliferative activity, and a massive inflammatory reaction of the peritoneum – that was diagnosed as a malignant ovarian tumor. Tumor biopsies were examined using morphological and immunohistochemical methods (with the р16, Ki-67, p53, CD 117, S 100, CD 34 markers). Immunohistochemical (IHC) studies were performed with formalin-fixed paraffin materials using the avidin-biotin-peroxidase method. Antibodies to estrogen receptor (ER), progesterone receptor (PR), cytokeratin 7 (CK7), cytokeratin 20 (CK20) and Wilms tumor protein 1 (WT1) were also used.Results. A thorough analysis of the clinical picture and a joint multidisciplinary discussion (gynecologist, oncologist, radiologist, etc.) made it possible to avoid diagnostic errors.Conclusion. These observations demonstrate the difficulties of differential diagnosis between ovarian metastases of uterine cancer and primary multiple ovarian and uterine cancer, as well between leiomyosarcoma and uterine myoma with high mitotic activity. Obviously, the change in diagnosis calls for a change in the treatment strategy.

scholarly journals Does the punishment fit the crime? Consequences and diagnosis of misspecified detection functions in Bayesian spatial capture-recapture modelling

2021 ◽  
Author(s):  
Soumen Dey ◽  
Richard Bischof ◽  
Pierre P. A. Dupont ◽  
Cyril Milleret
Keyword(s):  
Home Range ◽  
Space Use ◽  
Relative Bias ◽  
Diagnostic Tools ◽  
List Type ◽  
Detection Function ◽  
Density Estimates ◽  
Use Patterns ◽  
Wide Range ◽  
Capture Recapture

AbstractSpatial capture-recapture (SCR) is now used widely to estimate wildlife densities. At the core of SCR models lies the detection function, linking individual detection probability to the distance from its latent activity center. The most common function (half-normal) assumes a bivariate normal space use and consequently detection pattern. This is likely an oversimplification and misrepresentation of real-life animal space use patterns, but studies have reported that density estimates are relatively robust to misspecified detection functions. However, information about consequences of such misspecification on space use parameters (e.g. home range area), as well as diagnostic tools to reveal it are lacking.We simulated SCR data under six different detection functions, including the half-normal, to represent a wide range of space use patterns. We then fit three different SCR models, with the three simplest detection functions (half-normal, exponential and half-normal plateau) to each simulated data set. We evaluated the consequences of misspecification in terms of bias, precision and coverage probability of density and home range area estimates. We also calculated Bayesian p-values with respect to different discrepancy metrics to assess whether these can help identify misspecifications of the detection function.We corroborate previous findings that density estimates are robust to misspecifications of the detection function. However, estimates of home range area are prone to bias when the detection function is misspecified. When fitted with the half-normal model, average relative bias of 95% kernel home range area estimates ranged between −25% and 26% depending on the misspecification. In contrast, the half-normal plateau model (an extension of the half-normal) returned average relative bias that ranged between −26% and −4%. Additionally, we found useful heuristic patterns in Bayesian p-values to diagnose the misspecification in detection function.Our analytical framework and diagnostic tools may help users select a detection function when analyzing empirical data, especially when space use parameters (such as home range area) are of interest. We urge development of additional custom goodness of fit diagnostics for Bayesian SCR models to help practitioners identify a wider range of model misspecifications.

Finite-amplitude convection in the presence of an unsteady shear flow

1995 ◽  
Vol 287 ◽  
pp. 225-249 ◽  
Author(s):  
Philip Hall
Keyword(s):  
Shear Flow ◽  
Critical Size ◽  
Low Frequency ◽  
Nonlinear Effects ◽  
Finite Amplitude ◽  
Present Calculation ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boussinesq Fluid

The effect of an unsteady shear flow on the planform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the shear flow it is well-known, if non-Boussinesq effects can be neglected, that convection begins in the form of a supercritical bifurcation to rolls. Subcritical convection in the form of say hexagons can be induced by non-Boussinesq behaviour which destroys the symmetry of the basic state. Here it is found that the symmetry breaking effects associated with an unsteady shear flow are not sufficient to cause subcritical convection so the problem reduces to the determination of how the orientations of roll cells are modified by an unsteady shear flow. Recently Kelly & Hu (1993) showed that such a flow has a significant stabilizing effect on the linear stability problem and that, for a wide range of Prandtl numbers, the effect is most pronounced in the low-frequency limit. In the present calculation it is shown that the stabilizing effects found by Kelly & Hu (1993) do survive for most frequencies when nonlinear effects and imperfections are taken into account. However a critical size of the frequency is identified below which the Kelly & Hu (1993) conclusions no longer carry through into the nonlinear regime. For frequencies of size comparable with this critical size it is shown that the convection pattern changes in time. The cell pattern is found to be extremely complicated and straight rolls exist only for part of a period.

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