Yangian of the Queer Lie Superalgebra

NASA Astrophysics Data System (ADS)

Nazarov, Maxim

Consider the complex matrix Lie superalgebra with the standard generators , where . Define an involutory automorphism η of by . The twisted polynomial current Lie superalgebra has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a wide class of irreducible representations of the quantised algebra.

Beauty and the beast: Superconformal symmetry in a monster module

NASA Astrophysics Data System (ADS)

Dixon, L.; Ginsparg, P.; Harvey, J.

1988-06-01

Frenkel, Lepowsky, and Meurman have constructed a representation of the largest sporadic simple finite group, the Fischer-Griess monster, as the automorphism group of the operator product algebra of a conformal field theory with central charge c=24. In string terminology, their construction corresponds to compactification on a Z 2 asymmetric orbifold constructed from the torus R 24/∧, where ∧ is the Leech lattice. In this note we point out that their construction naturally embodies as well a larger algebraic structure, namely a super-Virasoro algebra with central charge ĉ=16, with the supersymmetry generator constructed in terms of bosonic twist fields.

Analysis of endomorphisms

NASA Astrophysics Data System (ADS)

Conti, Roberto; Hong, Jeong Hee; Szymański, Wojciech

2012-02-01

In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C* -algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra. Then we outline a powerful combinatorial approach to analysis of endomorphisms arising from permutation unitaries. The restricted Weyl group consists of automorphisms of this type. We also discuss the action of the restricted Weyl group on the diagonal MASA and its relationship with the automorphism group of the full two-sided n-shift. Finally, several open problems are presented.

One-dimensional super Calabi-Yau manifolds and their mirrors

NASA Astrophysics Data System (ADS)

Noja, S.; Cacciatori, S. L.; Piazza, F. Dalla; Marrani, A.; Re, R.

2017-04-01

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to P^1, namely the projective super space P^{.1|2} and the weighted projective super space W{P}_{(2)}^{.1|1} . Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces {P}^{.n|m} . We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of {P}^{.1|2} , whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of {P}^{.1|m} , discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that {P}^{.1|2} is self-mirror, whereas W{P}_{(2)}^{.1|1} has a zero dimensional mirror. Also, the mirror map for {P}^{.1|2} naturally endows it with a structure of N = 2 super Riemann surface.

Ecological and geographical regularities of changes in the biological activity of automorphic soils on the foothills and adjacent plains of the Central Caucasus region (Kabardino-Balkarian Republic)

NASA Astrophysics Data System (ADS)

Gorobtsova, O. N.; Khezheva, F. V.; Uligova, T. S.; Tembotov, R. Kh.

2015-03-01

The biochemical properties inherent to the main types of automorphic soils developed in different bioclimatic conditions of Elbrus and Terek variants of the vertical zonality within Kabardino-Balkaria were compared. The natural-climatic conditions of these variants noticeably affect the soil cover pattern. The ratio of the oxidase and hydrolase activities is sensitive to the moisture conditions in which these soils are formed. The redox processes are more active in drier conditions, whereas hydrolytic processes are more active under higher moisture. The level of the biological activity of the automorphic soils is estimated using the integral index of the ecological-biological soil status.

Adinkra (in)equivalence from Coxeter group representations: A case study

NASA Astrophysics Data System (ADS)

Chappell, Isaac; Gates, S. James; Hübsch, T.

2014-02-01

Using a MathematicaTM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the 𝒢ℛ(4, 4) algebra, closely related to the 𝒩 = 1 (simple) supersymmetry algebra in four-dimensional space-time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these 𝒢ℛ(4, 4) representations into three suggestive classes.

On the Inverse Mapping of the Formal Symplectic Groupoid of a Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2004-10-01

To each natural star product on a Poisson manifold $M$ we associate an antisymplectic involutive automorphism of the formal neighborhood of the zero section of the cotangent bundle of $M$. If $M$ is symplectic, this mapping is shown to be the inverse mapping of the formal symplectic groupoid of the star product. The construction of the inverse mapping involves modular automorphisms of the star product.

Automorphisms of Order Structures of Abelian Parts of Operator Algebras and Their Role in Quantum Theory

NASA Astrophysics Data System (ADS)

Hamhalter, Jan; Turilova, Ekaterina

2014-10-01

It is shown that any order isomorphism between the structures of unital associative JB subalgebras of JB algebras is given naturally by a partially linear Jordan isomorphism. The same holds for nonunital subalgebras and order isomorphisms preserving the unital subalgebra. Finally, we recover usual action of time evolution group on a von Neumann factor from group of automorphisms of the structure of Abelian subalgebras.

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ 12

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.

Here, we consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds’ automorphic form Φ 12, a modular form which exhibits automorphy for O(2, 26; Ζ). Here, we comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ 12

DOE PAGES

Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.; ...

2017-10-18

Here, we consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds’ automorphic form Φ 12, a modular form which exhibits automorphy for O(2, 26; Ζ). Here, we comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

The structure of EAP-groups and self-autopermutable subgroups.

PubMed

Housieni, Shima; Moghaddam, Mohammad Reza Rajabzadeh

2014-01-01

A subgroup H of a given group G is said to be autopermutable, if HH(α) = H(α)H for all α ∈ Aut(G). We also call H a self-autopermutable subgroup of G, when HH(α) = H(α)H implies that H(α) = H. Moreover, G is said to be EAP-group, if every subgroup of G is autopermutable. One notes that if α runs over the inner automorphisms of the group, one obtains the notions of conjugate-permutability, self-conjugate-permutability, and ECP-groups, which were studied by Foguel in 1997, Li and Meng in 2007, and Xu and Zhang in 2005, respectively. In the present paper, we determine the structure of a finite EAP-group when its centre is of index 4 in G. We also show that self-autopermutability and characteristic properties are equivalent for nilpotent groups.

Cyclotomic Gaudin Models: Construction and Bethe Ansatz

NASA Astrophysics Data System (ADS)

Vicedo, Benoît; Young, Charles

2016-05-01

To any finite-dimensional simple Lie algebra g and automorphism {σ: gto g we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of {U(g)^{⊗ N}} generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case {σ =id}. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.

Quantum deformations of conformal algebras with mass-like deformation parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek

1998-12-15

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2)more » reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.« less

Rholography, black holes and Scherk-Schwarz

DOE PAGES

Gaddam, Nava; Gnecchi, Alessandra; Vandoren, Stefan; ...

2015-06-10

We present a construction of a class of near-extremal asymptotically flat black hole solutions in four (or five) dimensional gauged supergravity with R-symmetry gaugings obtained from Scherk-Schwarz reductions on a circle. The entropy of these black holes is counted holographically by the well known MSW (or D1/D5) system, with certain twisted boundary conditions labeled by a twist parameter ρ. Here, we find that the corresponding (0, 4) (or (4, 4)) superconformal algebras are exactly those studied by Schwimmer and Seiberg, using a twist on the outer automorphism group. The interplay between R-symmetries, ρ-algebras and holography leads us to name ourmore » construction “Rholography”.« less

Rholography, black holes and Scherk-Schwarz

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaddam, Nava; Gnecchi, Alessandra; Vandoren, Stefan

We present a construction of a class of near-extremal asymptotically flat black hole solutions in four (or five) dimensional gauged supergravity with R-symmetry gaugings obtained from Scherk-Schwarz reductions on a circle. The entropy of these black holes is counted holographically by the well known MSW (or D1/D5) system, with certain twisted boundary conditions labeled by a twist parameter ρ. Here, we find that the corresponding (0, 4) (or (4, 4)) superconformal algebras are exactly those studied by Schwimmer and Seiberg, using a twist on the outer automorphism group. The interplay between R-symmetries, ρ-algebras and holography leads us to name ourmore » construction “Rholography”.« less

Asymptotic Behavior of Solutions of Systems of Neutral and Convolution Equations

NASA Astrophysics Data System (ADS)

Basit, Bolis; Günzler, Hans

1998-10-01

Suppose J=[α, ∞) for someα∈R or J=R and letXbe a Banach space. We study asymptotic behavior of solutions on J of neutral system of equations with values inX. This reduces to questions concerning the behavior of solutions of convolution equations (*)H∗Ω=b, whereH=(Hj, k) is anr×rmatrix,Hj, k∈D‧L1,b=(bj) andbj∈D‧(R, X), for 1⩽j, k⩽r. We prove that ifΩis a bounded uniformly continuous solution of (*) withbfrom some translation invariant suitably closed class A, thenΩbelongs to A, provided, for example, that det Hhas countably many zeros on R andc0⊄X. In particular, ifbis (asymptotically) almost periodic, almost automorphic or recurrent,Ωis too. Our results extend theorems of Bohr, Neugebauer, Bochner, Doss, Basit, and Zhikov and also, certain theorems of Fink, Madych, Staffans, and others. Also, we investigate bounded solutions of (*). This leads to an extension of the known classes of almost periodicity to larger classes called mean-classes. We explore mean-classes and prove that bounded solutions of (*) belong to mean-classes provided certain conditions hold. These results seem new even for the simplest difference equationΩ(t+1)-Ω(t)=b(t) with J=X=R andbStepanoff almost periodic.

BPS Jumping Loci are Automorphic

NASA Astrophysics Data System (ADS)

Kachru, Shamit; Tripathy, Arnav

2018-06-01

We show that BPS jumping loci-loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner—naturally appear as Fourier coefficients of (vector space-valued) automorphic forms. For the case of T 2 compactification, the jumping loci are governed by a modular form studied by Hirzebruch and Zagier, while the jumping loci in K3 compactification appear in a story developed by Oda and Kudla-Millson in arithmetic geometry. We also comment on some curious related automorphy in the physics of black hole attractors and flux vacua.

Weyl's search for a difference between 'physical' and 'mathematical' automorphisms

NASA Astrophysics Data System (ADS)

Scholz, Erhard

2018-02-01

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

NASA Astrophysics Data System (ADS)

Bibak, Khodakhast; Kapron, Bruce M.; Srinivasan, Venkatesh

2016-09-01

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an 'equivalent' form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.

Scalable and Axiomatic Ranking of Network Role Similarity

PubMed Central

Jin, Ruoming; Lee, Victor E.; Li, Longjie

2014-01-01

A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes according to how they interact with other nodes. Two nodes have the same role if they interact with equivalent sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithms known for graph automorphism are nonpolynomial. Moreover, since exact equivalence is rare, a more meaningful task is measuring the role similarity between any two nodes. This task is closely related to the structural or link-based similarity problem that SimRank addresses. However, SimRank and other existing similarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This paper makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a new similarity metric which satisfies these axioms and which can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all these axiomatic properties. We also introduce Iceberg RoleSim, a scalable algorithm which discovers all pairs with RoleSim scores above a user-defined threshold θ. We demonstrate the interpretative power of RoleSim on both both synthetic and real datasets. PMID:25383066

Automorphosis of higher plants on a 3-D clinostat

NASA Astrophysics Data System (ADS)

Hoson, T.; Kamisaka, S.; Yamashita, M.; Masuda, Y.

On a three-dimensional (3-D) clinostat, various plant organs developed statocytes capable of responding to the gravity vector. The graviresponse of primary roots of garden cress and maize grown on the clinostat was the same as the control roots, whereas that of maize coleoptiles was reduced. When maize seedlings were grown in the presence of 10^-4 M gibberellic acid and kinetin, the graviresponse of both roots and shoots was suppressed. The corresponding suppression of amyloplast development was observed in the clinostatted and the hormone-treated seedlings. Maize roots and shoots showed spontaneous curvatures in different portions on the 3-D clinostat. The hormone treatment did not significantly influence such an automorphic curvature. When the root cap was removed, maize roots did not curve gravitropically. However, the removal suppressed the automorphic curvatures only slightly. On the other hand, the removal of coleoptile tip did not influence its graviresponse, whereas the spontaneous curvature of decapitated coleoptiles on the clinostat was strongly suppressed. Also, cytochalasin B differently affected the gravitropic and the automorphic curvatures of maize roots and shoots. From these results it is concluded that the graviperception and the early processes of signal transmission are unnecessary for automorphoses under simulated microgravity conditions. Moreover, the results support the view that the amyloplasts act as statoliths probably via an interaction with microfilaments.

A Finite Element Analysis of a Class of Problems in Elasto-Plasticity with Hidden Variables.

DTIC Science & Technology

1985-09-01

RD-R761 642 A FINITE ELEMENT ANALYSIS OF A CLASS OF PROBLEMS IN 1/2 ELASTO-PLASTICITY MIlT (U) TEXAS INST FOR COMPUTATIONAL MECHANICS AUSTIN J T ODEN...end Subtitle) S. TYPE OF REPORT & PERIOD COVERED A FINITE ELEMENT ANALYSIS OF A CLASS OF PROBLEMS Final Report IN ELASTO-PLASTICITY WITH HIDDEN...aieeoc ede It neceeeary nd Identify by block number) ;"Elastoplasticity, finite deformations; non-convex analysis ; finite element methods, metal forming

Geochemical and petrographical characterization of fine-grained carbonate particles along proximal to distal transects

NASA Astrophysics Data System (ADS)

Turpin, Mélanie; Emmanuel, Laurent; Immenhauser, Adrian; Renard, Maurice

2012-12-01

The origin of carbonate ooze particles is often poorly understood. This is due to their polygenic origin and potential post-depositional alteration. Here, the outcome of a physical separation study with regard to different component classes of micritic carbonates is shown. The focus is on grain size and morphology, mineralogy and isotope signatures. Two contrasting proximal-to-distal transects were investigated: (1) the Miocene leeward margin of Great Bahama Bank (ODP Leg 166) and (2) the transition between the Maiella platform and the Umbria-Marche basin in central Italy near the Cenomanian-Turonian boundary. In both case settings, carbonate particles of biogenic origin include at least three groups of organisms: (i) planktonic foraminifera, (ii) calcareous nannofossils and (iii) fragments of unspecified neritic skeletal material. Two further particle types lack diagnostic structures, and based on particle size and mineralogy, are here referred to as (iv) macroparticles (5-20 μm, mainly xenomorphic) and (v) microparticles (< 12 μm, mainly automorphic to sub-automorphic). Macro- and microparticles represent 50 to 80% of the carbonate phase in slope and toe-of-slope domains and share characteristic carbon and oxygen isotope signatures. Macro- and microparticles are considered shallow-water precipitation products subsequently exported into the slope and toe-of-slope domains. Macroparticles are probably related to the fragmentation of neritic skeletal components while microparticles point to inorganic and/or bioinduced precipitation in the water column. In some cases, macro- and microparticles may have an early diagenetic origin. The identification of the origin of fine-grained particles allows for a quantitative assessment of exported, in situ and diagenetic carbonate materials in periplatform environments. The data shown here represent an important step towards a more complete characterization of carbonate ooze and micrite.

Water-soluble low-molecular-weight organic acids in automorphic loamy soils of the tundra and taiga zones

NASA Astrophysics Data System (ADS)

Shamrikova, E. V.; Gruzdev, I. V.; Punegov, V. V.; Khabibullina, F. M.; Kubik, O. S.

2013-06-01

The formation features of water-soluble low-molecular-weight organic acids (LMWOAs) in a zonal series of automorphic soils on loose silicate rocks from the middle taiga to the southern tundra (typical podzolic, gley-podzolic, and surface-gley tundra soils) were first revealed by gas chromatography mass spectrometry and gas-liquid chromatography. The content of LMWOAs varies within the range of 1-14 mg/dm3, which corresponds to 1-5% of the total carbon of the water-soluble soil organic matter. It has been shown that a subzonal feature of gley-podzolic soils in the northern taiga is the high content of LMWOAs, including primarily the strongest aliphatic hydroxyl acids. Possible mechanisms of their formation and accumulation in soils have been considered.

The quantum theory of free automorphic fields

NASA Astrophysics Data System (ADS)

Banach, R.

1980-06-01

Heuristic spectral theory is developed for a symmetric operator on the universal covering space of a multiply connected static spacetime and is used to construct the quantum field theory of a multiplet of scalar fields in the customary sum-over-modes fashion. The non-local symmetries necessary to the theory are explicitly constructed, as are the projection on the field operators. The non-existence of a standard charge conjugation for certain types of representation is noted. Gauge transformations are used to give a simple and complete classification of automorphic field theories. The relationship between the unprojected and projected field algebras is clarified, and the implications for Fock space (vacuum degeneracy, etc.) are discussed - earlier work being criticized. The analogy to black hole physics is pointed out, and the possible role of the Reeh-Schlieder theorems is speculated upon.

Climate and soil salinity in the deserts of Central Asia

NASA Astrophysics Data System (ADS)

Pankova, E. I.; Konyushkova, M. V.

2013-07-01

A comparative analysis of climatic and soil salinity characteristics of the deserts of Central Asia, including deserts of the Turan Depression, the Gobi Desert, and deserts of the Dzungar and Tarim depressions was performed. The climatic characteristics—the degree of aridity, the degree of continentality, and the amount and regime of precipitation—are different in these deserts. No direct relationships between the areas occupied by the automorphic salt-affected soils and the aridity of the climate are observed in the studied regions. In the automorphic landscapes of Asian deserts, the degree and chemistry of the soil salinization and the distribution of salt-affected soils are controlled by the history of the particular territories rather than by their modern climatic conditions. The presence and properties of the salt-bearing rocks and the eolian migration of salts play the most significant role. The deficit of moisture in the modern climate favors the preservation of salt accumulations in places of their origin. The specific features of the climate, including the regime of precipitation, affect the redistribution of salts in the profiles of automorphic salt-affected soils. An increase in the degree of climatic continentality is accompanied by the decrease in the intensity of weathering and initial accumulation of salts. A different situation is observed in the soils of hydromorphic desert landscapes, in which the degree of salinity of the surface horizons and the area occupied by salt-affected soils are directly influenced by the modern climatic conditions.

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

On the spring and mass of the Dirac oscillator

NASA Technical Reports Server (NTRS)

Crawford, James P.

1993-01-01

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.

BPS states in N = 2 supersymmetric G2 and F4 models

NASA Astrophysics Data System (ADS)

Ahl Laamara, R.; Mellal, O.; Saidi, E. H.

2017-07-01

In BPS quiver theory of N = 2 supersymmetric pure gauge models with gauge invariance G, primitive BPS quivers Q0G are of two types: Q0ADE and Q0BCFG. In this study, we first show that Q0ADE have outer-automorphism symmetries inherited from the outer-automorphisms of the Dynkin diagrams of ADE Lie algebras. Then, we extend the usual folding operation of Dynkin diagrams ADE → BCFG to obtain the two following things: (i) relate Q0BCFG quivers and their mutations to the Q0ADE ones and their mutations; and (ii) link the BPS chambers of the N = 2ADE theories with the corresponding BCFG ones. As an illustration of this construction, we derive the BPS and anti-BPS states of the strong chambers QstgG2 and QstgF4 of the 4d N = 2 pure G2 and F4 gauge models.

Rough Finite State Automata and Rough Languages

NASA Astrophysics Data System (ADS)

Arulprakasam, R.; Perumal, R.; Radhakrishnan, M.; Dare, V. R.

2018-04-01

Sumita Basu [1, 2] recently introduced the concept of a rough finite state (semi)automaton, rough grammar and rough languages. Motivated by the work of [1, 2], in this paper, we investigate some closure properties of rough regular languages and establish the equivalence between the classes of rough languages generated by rough grammar and the classes of rough regular languages accepted by rough finite automaton.

Supersymmetric M3-branes and G2 manifolds

NASA Astrophysics Data System (ADS)

Cvetič, M.; Gibbons, G. W.; Lü, H.; Pope, C. N.

2002-01-01

We obtain a generalisation of the original complete Ricci-flat metric of G2 holonomy on R4×S 3 to a family with a nontrivial parameter λ. For generic λ the solution is singular, but it is regular when λ={-1,0,+1}. The case λ=0 corresponds to the original G2 metric, and λ={-1,1} are related to this by an S3 automorphism of the SU(2) 3 isometry group that acts on the S3× S3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D=11 supergravity, where the transverse space is a deformation of this class of G2 metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G2 holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.

Entanglement entropy for (3+1)-dimensional topological order with excitations

NASA Astrophysics Data System (ADS)

Wen, Xueda; He, Huan; Tiwari, Apoorv; Zheng, Yunqin; Ye, Peng

2018-02-01

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group G and its group 4-cocycle ω ∈H4[G ;U(1 ) ] up to group automorphisms. We find that each topological excitation contributes a universal constant lndi to the entanglement entropy, where di is the quantum dimension that depends on both the structure of the excitation and the data (G ,ω ) . The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory (G ,ω ) . In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles ω from the others.

Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

NASA Astrophysics Data System (ADS)

Fehér, L.; Klimčík, C.

2012-07-01

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider IIIb system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the IIIb phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the IIIb system in terms of flat SU(n) connections on the one-holed torus.

Which Q-analogue of the squeezed oscillator?

NASA Technical Reports Server (NTRS)

Solomon, Allan I.

1993-01-01

The noise (variance squared) of a component of the electromagnetic field - considered as a quantum oscillator - in the vacuum is equal to one half, in appropriate units (taking Planck's constant and the mass and frequency of the oscillator all equal to 1). A practical definition of a squeezed state is one for which the noise is less than the vacuum value - and the amount of squeezing is determined by the appropriate ratio. Thus the usual coherent (Glauber) states are not squeezed, as they produce the same variance as the vacuum. However, it is not difficult to define states analogous to coherent states which do have this noise-reducing effect. In fact, they are coherent states in the more general group sense but with respect to groups other than the Heisenberg-Weyl Group which defines the Glauber states. The original, conventional squeezed state in quantum optics is that associated with the group SU(1,1). Just as the annihilation operator a of a single photon mode (and its hermitian conjugate a, the creation operator) generates the Heisenberg Weyl algebra, so the pair-photon operator a(sup 2) and its conjugate generates the algebra of the group SU(1,1). Another viewpoint, more productive from the calculational stance, is to note that the automorphism group of the Heisenberg-Weyl algebra is SU(1,1). Needless to say, each of these viewpoints generalizes differently to the quantum group context. Both are discussed. The following topics are addressed: conventional coherent and squeezed states; eigenstate definitions; exponential definitions; algebra (group) definitions; automorphism group definition; example: signal-to-noise ratio; q-coherent and q-squeezed states; M and P q-bosons; eigenstate definitions; exponential definitions; algebra (q-group) definitions; and automorphism q-group definition.

Assessment of the postagrogenic transformation of soddy-podzolic soils: Cartographic and analytic support

NASA Astrophysics Data System (ADS)

Sorokina, N. P.; Kozlov, D. N.; Kuznetsova, I. V.

2013-10-01

The results of experimental studies of the postagrogenic transformation of loamy soddy-podzolic soils on the southern slope of the Klin-Dmitrov Moraine Ridge are discussed. A chronosequence of soils (arable soils (cropland)-soils under fallow with meadow vegetation-soils under secondary forests of different ages-soils under a conventionally initial native forest) was examined, and the stages of the postagrogenic transformation of the automorphic soddy-podzolic soils were identified. The differentiation of the former plow horizon into the A1 and A1A2 horizons (according to the differences in the humus content, texture, and acidity) served as the major criterion of the soil transformation. A stage of textural differentiation with clay depletion from the uppermost layer was identified in the soils of the 20- to 60-year-old fallows. The specificity of the postagrogenic transformation of the soils on the slopes was demonstrated. From the methodological point of view, it was important to differentiate between the chronosequences of automorphic and semihydromorphic soils of the leveled interfluves and the soils of the slopes. For this purpose, a series of maps reflecting the history of the land use and the soil cover pattern was analyzed. The cartographic model included the attribute data of the soil surveys, the cartographic sources (a series of historical maps of the land use, topographic maps, remote sensing data, and a digital elevation model), and two base maps: (a) the integral map of the land use and (b) the map of the soil combinations with the separation of the zonal automorphic, semihydromorphic, and erosional soil combinations. This scheme served as a matrix for the organization and analysis of the already available and new materials.

Splitting of the weak hypercharge quantum

NASA Astrophysics Data System (ADS)

Nielsen, H. B.; Brene, N.

1991-08-01

The ratio between the weak hypercharge quantum for particles having no coupling to the gauge bosons corresponding to the semi-simple component of the gauge group and the smallest hypercharge quantum for particles that do have such couplings is exceptionally large for the standard model, considering its rank. To compare groups with respect to this property we propose a quantity χ which depends on the rank of the group and the splitting ratio of the hypercharge(s) to be found in the group. The quantity χ has maximal value for the gauge group of the standard model. This suggests that the hypercharge splitting may play an important rôle either in the origin of the gauge symmetry at a fundamental scale or in some kind of selection mechanism at a scale perhaps nearer to the experimental scale. Such a selection mechanism might be what we have called confusion which removes groups with many (so-called generalized) automorphisms. The quantity χ tends to be large for groups with few generalized automorphisms.

On the construction of unitary quantum group differential calculus

NASA Astrophysics Data System (ADS)

Pyatov, Pavel

2016-10-01

We develop a construction of the unitary type anti-involution for the quantized differential calculus over {{GL}}q(n) in the case | q| =1. To this end, we consider a joint associative algebra of quantized functions, differential forms and Lie derivatives over {{GL}}q(n)/{{SL}}q(n), which is bicovariant with respect to {{GL}}q(n)/{{SL}}q(n) coactions. We define a specific non-central spectral extension of this algebra by the spectral variables of three matrices of the algebra generators. In the spectrally expended algebra, we construct a three-parametric family of its inner automorphisms. These automorphisms are used for the construction of the unitary anti-involution for the (spectrally extended) calculus over {{GL}}q(n). This work has been funded by the Russian Academic Excellence Project ‘5-100’. The results of section 5 (propositions 5.2, 5.3 and theorem 5.5) have been obtained under support of the RSF grant No.16-11-10160.

Root uptake of 137Cs by natural and semi-natural grasses as a function of texture and moisture of soils.

PubMed

Grytsyuk, N; Arapis, G; Davydchuk, V

2006-01-01

This work studies the dependence of 137Cs root uptake on the structure of landscape, especially on texture and moisture of soils, under natural conditions, on abandoned radiopolluted lands in Northern Ukraine. Researches were carried out on a wide range of landscape conditions, at various levels of 137Cs contamination (from 20 up to 5000 kBqm(-2)), with different types of soils (approx. 20 soil varieties), which differ in texture, granulometric composition, degrees of gleyization and water regime, and anthropogenic transformation. The results showed that transfer factor (TF) values of 137Cs differ 50 times for the natural grassy coenoses and 8 times for the semi-natural ones. The lowest 137Cs TF values were measured in the herbages of dry meadows at automorphous loamy soils, while the highest were observed in wetland meadows at organic soils. Finally, the correlation between 137Cs TF values and granulometric composition of soil was determined for both automorphic and hydromorphic mineral soils.

Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators

NASA Astrophysics Data System (ADS)

Alekseev, Anton; Naef, Florian; Xu, Xiaomeng; Zhu, Chenchang

2018-03-01

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern-Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as p= < F, F> where F is the curvature 2-form and < \\cdot , \\cdot > is an invariant scalar product on the corresponding Lie algebra g. The descent for p gives rise to an element ω =ω _3+ω _2+ω _1+ω _0 of mixed degree. The 3-form part ω _3 is the Chern-Simons form. The 2-form part ω _2 is known as the Wess-Zumino action in physics. The 1-form component ω _1 is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components ω _1 and ω _0. Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara-Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara-Vergne equation F is mapped to ω _1=C(F). Furthermore, the component ω _0 is related to the associator Φ corresponding to F. It is surprising that while F and Φ satisfy the highly nonlinear twist and pentagon equations, the elements ω _1 and ω _0 solve the linear descent equation.

Holomorphic projections and Ramanujan’s mock theta functions

PubMed Central

Imamoğlu, Özlem; Raum, Martin; Richter, Olav K.

2014-01-01

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan’s mock theta functions. PMID:24591582

A new class of finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2014-02-01

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

SH c realization of minimal model CFT: triality, poset and Burge condition

NASA Astrophysics Data System (ADS)

Fukuda, M.; Nakamura, S.; Matsuo, Y.; Zhu, R.-D.

2015-11-01

Recently an orthogonal basis of {{W}}_N -algebra (AFLT basis) labeled by N-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH c which is universal for any N. We show that it has an {{S}}_3 automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by N or M Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH c . Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the N-Burge condition in the Hilbert space.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Maximum likelihood estimation of finite mixture model for economic data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-06-01

Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.

The first law of black hole mechanics for fields with internal gauge freedom

NASA Astrophysics Data System (ADS)

Prabhu, Kartik

2017-02-01

We derive the first law of black hole mechanics for physical theories based on a local, covariant and gauge-invariant Lagrangian where the dynamical fields transform non-trivially under the action of some internal gauge transformations. The theories of interest include General Relativity formulated in terms of tetrads, Einstein-Yang-Mills theory and Einstein-Dirac theory. Since the dynamical fields of these theories have some internal gauge freedom, we argue that there is no natural group action of diffeomorphisms of spacetime on such dynamical fields. In general, such fields cannot even be represented as smooth, globally well-defined tensor fields on spacetime. Consequently the derivation of the first law by Iyer and Wald cannot be used directly. Nevertheless, we show how such theories can be formulated on a principal bundle and that there is a natural action of automorphisms of the bundle on the fields. These bundle automorphisms encode both spacetime diffeomorphisms and internal gauge transformations. Using this reformulation we define the Noether charge associated to an infinitesimal automorphism and the corresponding notion of stationarity and axisymmetry of the dynamical fields. We first show that we can define certain potentials and charges at the horizon of a black hole so that the potentials are constant on the bifurcate Killing horizon, giving a generalised zeroth law for bifurcate Killing horizons. We further identify the gravitational potential and perturbed charge as the temperature and perturbed entropy of the black hole which gives an explicit formula for the perturbed entropy analogous to the Wald entropy formula. We then obtain a general first law of black hole mechanics for such theories. The first law relates the perturbed Hamiltonians at spatial infinity and the horizon, and the horizon contributions take the form of a ‘potential times perturbed charge’ term. We also comment on the ambiguities in defining a prescription for the total entropy for black holes.

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

NASA Astrophysics Data System (ADS)

Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An

2012-12-01

This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation.

PubMed

Gao, Fangzheng; Yuan, Ye; Wu, Yuqiang

2016-09-01

This paper studies the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems in feedforward-like form subject to inputs saturation. Under the weaker homogeneous condition on systems growth, a saturated finite-time control scheme is developed by exploiting the adding a power integrator method, the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed saturated controller guarantees that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of saturated finite-time control for vertical wheel on rotating table is solved. Simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Flipping Freshman Mathematics

ERIC Educational Resources Information Center

Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

2015-01-01

Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies.

PubMed

Huang, Yangxin; Lu, Xiaosun; Chen, Jiaqing; Liang, Juan; Zangmeister, Miriam

2017-10-27

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.

Algorithms for computations of Loday algebras' invariants

NASA Astrophysics Data System (ADS)

Hussain, Sharifah Kartini Said; Rakhimov, I. S.; Basri, W.

2017-04-01

The paper is devoted to applications of some computer programs to study structural determination of Loday algebras. We present how these computer programs can be applied in computations of various invariants of Loday algebras and provide several computer programs in Maple to verify Loday algebras' identities, the isomorphisms between the algebras, as a special case, to describe the automorphism groups, centroids and derivations.

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

NASA Astrophysics Data System (ADS)

Huang, Shipei; Xiang, Zhengrong

2018-06-01

This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.

Finite Geometries in Quantum Theory:. from Galois (fields) to Hjelmslev (rings)

NASA Astrophysics Data System (ADS)

Saniga, Metod; Planat, Michel

Geometries over Galois fields (and related finite combinatorial structures/algebras) have recently been recognized to play an ever-increasing role in quantum theory, especially when addressing properties of mutually unbiased bases (MUBs). The purpose of this contribution is to show that completely new vistas open up if we consider a generalized class of finite (projective) geometries, viz. those defined over Galois rings and/or other finite Hjelmslev rings. The case is illustrated by demonstrating that the basic combinatorial properties of a complete set of MUBs of a q-dimensional Hilbert space { H}q, q = pr with p being a prime and r a positive integer, are qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p2 and rank r. The q vectors of a basis of { H}q correspond to the q points of a (so-called) neighbour class and the q + 1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic. Although this remarkable analogy is still established at the level of cardinalities only, we currently work on constructing an explicit mapping by associating a MUB to each neighbour class of the points of the conic and a state vector of this MUB to a particular point of the class. Further research in this direction may prove to be of great relevance for many areas of quantum information theory, in particular for quantum information processing.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

1977-01-01

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

Isopermutation group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muktibodh, A. S.

2015-03-10

The concept of ‘Isotopy’ as formulated by Ruggero Maria Santilli [1, 2, 3] plays a vital role in the development of Iso mathematics. Santilli defined iso-fields of characteristic zero. In this paper we extend this definition to define Iso-Galois fields [4] which are essentially of non-zero characteristic. Isotopically isomorphic realizations of a group define isopermutation group which gives a clear cut distinction between automorphic groups and isotopic groups.

Instantons in string theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahlén, Olof, E-mail: olof.ahlen@aei.mpg.de

2015-12-17

These proceedings from the second Caesar Lattes meeting in Rio de Janeiro 2015 are a brief introduction to how automorphic forms appear in the low energy effective action of maximally supersymmetric string theory. The explicit example of the R{sup 4}-interaction of type IIB string theory in ten dimensions is discussed. Its Fourier expansion is interpreted in terms of perturbative and non-perturbative contributions to the four graviton amplitude.

Generalised Spin Dynamics and Induced Bounds of Automorphic [A]nX, [AX]n NMR Systems via Dual Tensorial Sets: An Invariant Cardinality Role for CFP

NASA Astrophysics Data System (ADS)

Temme, Francis P.

For uniform spins and their indistinguishable point sets of tensorial bases defining automorphic group-based Liouvillian NMR spin dynamics, the role of recursively-derived coefficients of fractional parentage (CFP) bijections and Schur duality-defined CFP(0)(n) ≡ ¦GI¦(n) group invariant cardinality is central both to understanding the impact of time-reversal invariance(TRI) spin physics, and to analysis as density-matrix formalisms over democratic recoupled (DR) dual tensorial sets, {T{ṽ}k(11.1)(SU2 × ln)}. Over abstract spin space, these tensorial sets are (ṽ) invariant-theoretic forms which lie beyond the Liouvillian graph recoupling and Racah-forms envisaged by Sanctuary [1]. This is a direct consequence of the dominance of the ln group. It leads to new views on the value of projective group actions as mappings over specialised Liouvillian carrier spaces, and on the need for the replacement of Racah-Wigner (R-W) orthogonality for distinct point sets, by criteria based on explicit properties of invariants [J. Phys.: Math. & Theor. A 41, 015210 (2008)] for multiple invariant systems. Ũ × P group actions over disjoint (L) carrier subspaces, leading to exclusively combinatorial views of the nature of quantal completeness for indistinguishable point-based tensorial sets. Such generalised invariant-theoretic approaches lie beyond the range of Lévi-Civitá generator views, or of Lévy-Leblond and Lévy-Nahas [9] with its additional cyclic-commutators defining mono-invariant DR forms. Comparison of the latter with generalised multiple-invariant techniques provides an answer to the question of precisely why [A]n≥4(X) and [AX]n≥4 NMR system spin dynamics are not ameniable to conventional R-W analysis of recoupled discrete-point tensorial systems. Our work augments earlier Hilbert space views, both of Louck and Biedenharn [21] on boson pattern projective mapping, and of Corio [19]. The roles of recent ln group action and (λ ⊢ n)-Schur combinatorial concepts, as well as of polyhedral-combinatorial modelling over invariance algebras, contribute significantly to our understanding of invariant-based techniques of Liouville dual tensorial sets for automorphic NMR spin physics.1

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

A Matter of Classes: Stratifying Health Care Populations to Produce Better Estimates of Inpatient Costs

PubMed Central

Rein, David B

2005-01-01

Objective To stratify traditional risk-adjustment models by health severity classes in a way that is empirically based, is accessible to policy makers, and improves predictions of inpatient costs. Data Sources Secondary data created from the administrative claims from all 829,356 children aged 21 years and under enrolled in Georgia Medicaid in 1999. Study Design A finite mixture model was used to assign child Medicaid patients to health severity classes. These class assignments were then used to stratify both portions of a traditional two-part risk-adjustment model predicting inpatient Medicaid expenditures. Traditional model results were compared with the stratified model using actuarial statistics. Principal Findings The finite mixture model identified four classes of children: a majority healthy class and three illness classes with increasing levels of severity. Stratifying the traditional two-part risk-adjustment model by health severity classes improved its R2 from 0.17 to 0.25. The majority of additional predictive power resulted from stratifying the second part of the two-part model. Further, the preference for the stratified model was unaffected by months of patient enrollment time. Conclusions Stratifying health care populations based on measures of health severity is a powerful method to achieve more accurate cost predictions. Insurers who ignore the predictive advances of sample stratification in setting risk-adjusted premiums may create strong financial incentives for adverse selection. Finite mixture models provide an empirically based, replicable methodology for stratification that should be accessible to most health care financial managers. PMID:16033501

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

Some Classes of Imperfect Information Finite State-Space Stochastic Games with Finite-Dimensional Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

McEneaney, William M.

2004-08-15

Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity ofmore » an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.« less

Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation.

PubMed

Yu, Jinpeng; Zhao, Lin; Yu, Haisheng; Lin, Chong; Dong, Wenjie

2017-08-22

This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

Closed form solution for the finite anti-plane shear field for a class of hyperelastic incompressible brittle solids

NASA Astrophysics Data System (ADS)

Stolz, Claude

2010-12-01

The equilibrium solution of a damaged zone in finite elasticity is given for a class of hyperelastic materials which does not suffer tension when a critical stretching value is reached. The study is made for a crack in anti-plane shear loading condition. The prescribed loading is that of linearized elastostatics conditions at infinity. The geometry of the damaged zone is found and the stationary propagation is discussed when the inertia terms can be neglected.

A training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems.

PubMed

Kuntanapreeda, S; Fullmer, R R

1996-01-01

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.

A numerical analysis of contact and limit-point behavior in a class of problems of finite elastic deformation

NASA Technical Reports Server (NTRS)

Endo, T.; Oden, J. T.; Becker, E. B.; Miller, T.

1984-01-01

Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.

A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grines, V Z; Pochinka, O V; Kapkaeva, S Kh

In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles.

Rheological Properties of Automorphic and Semihydromorphic Cryometamorphic Northern Taiga Soils in Northeastern European Russia (Komi Republic)

NASA Astrophysics Data System (ADS)

Kholopov, Yu. V.; Khaidapova, D. D.; Lapteva, E. M.

2018-04-01

Soil pastes at the water content corresponding to the maximum swelling of samples from different genetic horizons of cryometamorphic soils―surface-gleyic iron-illuvial svetlozem (Folic Albic Stagnosol) and peaty and peat humus-impregnated gleyic svetlozems (Histic Gleyic Stagnosols)―have been studied with an MCR-302 modular rheometer (Anton Paar, Austria). It has been found that the strongest interparticle bonds are formed in the horizons of cryometamorphic soils characterized by high contents of humic substances and organomineral Al-Fe-humus compounds. These are horizons of podzol microprofile (Eg and BHF) in iron-illuvial svetlozem and a humus-impregnated horizon (ELhi,g) in peaty and peat svetlozems. Organomineral Al-Fe-humus compounds, as well as the seasonal freezing of soils, determine the elastic-brittle character of interparticle interactions. The contents of clay fractions, exchangeable bases, and organic and organomineral substances impart viscoelastic properties to these contacts. An enhancement of elastic-brittle properties of soil is observed under the impact of gleying and freezing. The threefold decrease of the structural interaction parameter (∫ Z) when going from automorphic to semihydromorphic conditions indicates a decrease in the resistance of peaty and peat svetlozems to mechanical loads under increasing hydromorphism compared to iron-illuvial svetlozems.

Covariant path integrals on hyperbolic surfaces

NASA Astrophysics Data System (ADS)

Schaefer, Joe

1997-11-01

DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).

Differentialless geometry of plane curves

NASA Astrophysics Data System (ADS)

Latecki, Longin J.; Rosenfeld, Azriel

1997-10-01

We introduce a class of planar arcs and curves, called tame arcs, which is general enough to describe the boundaries of planar real objects. A tame arc can have smooth parts as well as sharp corners; thus a polygonal arc is tame. On the other hand, this class of arcs is restrictive enough to rule out pathological arcs which have infinitely many inflections or which turn infinitely often: a tame arc can have only finitely many inflections, and its total absolute turn must be finite. In order to relate boundary properties of discrete objects obtained by segmenting digital images to the corresponding properties of their continuous originals, the theory of tame arcs is based on concepts that can be directly transferred from the continuous to the discrete domain. A tame arc is composed of a finite number of supported arcs. We define supported digital arcs and motivate their definition by the fact that hey can be obtained by digitizing continuous supported arcs. Every digital arc is tame, since it contains a finite number of points, and therefore it can be decomposed into a finite number of supported digital arcs.

The Finite Lamplighter Groups: A Guided Tour

ERIC Educational Resources Information Center

Siehler, Jacob A.

2012-01-01

In this article, we present a family of finite groups, which provide excellent examples of the basic concepts of group theory. To work out the center, conjuagacy classes, and commutators of these groups, all that's required is a bit of linear algebra.

Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

PubMed

Kühn, Reimer

2016-04-01

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

PubMed

Sun, Yumei; Chen, Bing; Lin, Chong; Wang, Honghong

2017-09-18

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.

On Maximal Subalgebras and the Hypercentre of Lie Algebras.

ERIC Educational Resources Information Center

Honda, Masanobu

1997-01-01

Derives two sufficient conditions for a finitely generated Lie algebra to have the nilpotent hypercenter. Presents a relatively large class of generalized soluble Lie algebras. Proves that if a finitely generated Lie algebra has a nilpotent maximal subalgebra, the Fitting radical is nilpotent. (DDR)

Computer program analyzes Buckling Of Shells Of Revolution with various wall construction, BOSOR

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1968-01-01

Computer program performs stability analyses for a wide class of shells without unduly restrictive approximations. The program uses numerical integration, finite difference of finite element techniques to solve with reasonable accuracy almost any buckling problem for shells exhibiting orthotropic behavior.

A comparison of the finite difference and finite element methods for heat transfer calculations

NASA Technical Reports Server (NTRS)

Emery, A. F.; Mortazavi, H. R.

1982-01-01

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching.

PubMed

Wu, Yuanyuan; Cao, Jinde; Li, Qingbo; Alsaedi, Ahmed; Alsaadi, Fuad E

2017-01-01

This paper deals with the finite-time synchronization problem for a class of uncertain coupled switched neural networks under asynchronous switching. By constructing appropriate Lyapunov-like functionals and using the average dwell time technique, some sufficient criteria are derived to guarantee the finite-time synchronization of considered uncertain coupled switched neural networks. Meanwhile, the asynchronous switching feedback controller is designed to finite-time synchronize the concerned networks. Finally, two numerical examples are introduced to show the validity of the main results. Copyright © 2016 Elsevier Ltd. All rights reserved.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Klein-Weyl's program and the ontology of gauge and quantum systems

NASA Astrophysics Data System (ADS)

Catren, Gabriel

2018-02-01

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program-that we call the Klein-Weyl program-for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a "structure-endowed entity" equipped with a "group of automorphisms". First, we analyze what Weyl calls the "problem of relativity" in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are "indices characterizing representations of groups" ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

NASA Technical Reports Server (NTRS)

Wu, Xinen; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.

Realization of Uq(sp(2n)) within the Differential Algebra on Quantum Symplectic Space

NASA Astrophysics Data System (ADS)

Zhang, Jiao; Hu, Naihong

2017-10-01

We realize the Hopf algebra U_q({sp}_{2n}) as an algebra of quantum differential operators on the quantum symplectic space X(f_s;R) and prove that X(f_s;R) is a U_q({sp}_{2n})-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of U_q({sp}_{2n}).

Morera-type theorems in the hyperbolic disc

NASA Astrophysics Data System (ADS)

Volchkov, V. V.; Volchkov, V. V.

2018-02-01

Let G be the group of conformal automorphisms of the unit disc {D}=\\{z\\in{C}\\colon \\vert z\\vert<1\\}. We study the problem of the holomorphicity of functions f on {D} satisfying the equation where γ\\varrho=\\{z\\in{C}\\colon \\vert z\\vert=\\varrho\\} and ρ\\in(0,1) is fixed. We find exact conditions for holomorphicity in terms of the boundary behaviour of such functions. A by-product of our work is a new proof of the Berenstein-Pascuas two-radii theorem.

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

A Ring Construction Using Finite Directed Graphs

ERIC Educational Resources Information Center

Bardzell, Michael

2012-01-01

In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

A Typology for Finite Groups

ERIC Educational Resources Information Center

Tou, Erik R

2013-01-01

This project classifies groups of small order using a group's center as the key feature. Groups of a given order "n" are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups…

Finite Mixture Multilevel Multidimensional Ordinal IRT Models for Large Scale Cross-Cultural Research

ERIC Educational Resources Information Center

de Jong, Martijn G.; Steenkamp, Jan-Benedict E. M.

2010-01-01

We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while…

Finite element analysis of maxillary bone stress caused by Aramany Class IV obturator prostheses.

PubMed

Miyashita, Elcio Ricardo; Mattos, Beatriz Silva Câmara; Noritomi, Pedro Yoshito; Navarro, Hamilton

2012-05-01

The retention of an Aramany Class IV removable partial dental prosthesis can be compromised by a lack of support. The biomechanics of this obturator prosthesis result in an unusual stress distribution on the residual maxillary bone. This study evaluated the biomechanics of an Aramany Class IV obturator prosthesis with finite element analysis and a digital 3-dimensional (3-D) model developed from a computed tomography scan; bone stress was evaluated according to the load placed on the prosthesis. A 3-D model of an Aramany Class IV maxillary resection and prosthesis was constructed. This model was used to develop a finite element mesh. A 120 N load was applied to the occlusal and incisal platforms corresponding to the prosthetic teeth. Qualitative analysis was based on the scale of maximum principal stress; values obtained through quantitative analysis were expressed in MPa. Under posterior load, tensile and compressive stresses were observed; the tensile stress was greater than the compressive stress, regardless of the bone region, and the greatest compressive stress was observed on the anterior palate near the midline. Under an anterior load, tensile stress was observed in all of the evaluated bone regions; the tensile stress was greater than the compressive stress, regardless of the bone region. The Aramany Class IV obturator prosthesis tended to rotate toward the surgical resection when subjected to posterior or anterior loads. The amount of tensile and compressive stress caused by the Aramany Class IV obturator prosthesis did not exceed the physiological limits of the maxillary bone tissue. (J Prosthet Dent 2012;107:336-342). Copyright © 2012 The Editorial Council of the Journal of Prosthetic Dentistry. Published by Mosby, Inc. All rights reserved.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

NASA Technical Reports Server (NTRS)

Kou, Yu; Lin, Shu; Fossorier, Marc

1999-01-01

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Sliding mode control method having terminal convergence in finite time

NASA Technical Reports Server (NTRS)

Venkataraman, Subramanian T. (Inventor); Gulati, Sandeep (Inventor)

1994-01-01

An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters.

Finite-time resilient decentralized control for interconnected impulsive switched systems with neutral delay.

PubMed

Ren, Hangli; Zong, Guangdeng; Hou, Linlin; Yang, Yi

2017-03-01

This paper is concerned with the problem of finite-time control for a class of interconnected impulsive switched systems with neutral delay in which the time-varying delay appears in both the state and the state derivative. The concepts of finite-time boundedness and finite-time stability are respectively extended to interconnected impulsive switched systems with neutral delay for the first time. By applying the average dwell time method, sufficient conditions are first derived to cope with the problem of finite-time boundedness and finite-time stability for interconnected impulsive switched systems with neutral delay. In addition, the purpose of finite-time resilient decentralized control is to construct a resilient decentralized state-feedback controller such that the closed-loop system is finite-time bounded and finite-time stable. All the conditions are formulated in terms of linear matrix inequalities to ensure finite-time boundedness and finite-time stability of the given system. Finally, an example is presented to illustrate the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Mixture models in diagnostic meta-analyses--clustering summary receiver operating characteristic curves accounted for heterogeneity and correlation.

PubMed

Schlattmann, Peter; Verba, Maryna; Dewey, Marc; Walther, Mario

2015-01-01

Bivariate linear and generalized linear random effects are frequently used to perform a diagnostic meta-analysis. The objective of this article was to apply a finite mixture model of bivariate normal distributions that can be used for the construction of componentwise summary receiver operating characteristic (sROC) curves. Bivariate linear random effects and a bivariate finite mixture model are used. The latter model is developed as an extension of a univariate finite mixture model. Two examples, computed tomography (CT) angiography for ruling out coronary artery disease and procalcitonin as a diagnostic marker for sepsis, are used to estimate mean sensitivity and mean specificity and to construct sROC curves. The suggested approach of a bivariate finite mixture model identifies two latent classes of diagnostic accuracy for the CT angiography example. Both classes show high sensitivity but mainly two different levels of specificity. For the procalcitonin example, this approach identifies three latent classes of diagnostic accuracy. Here, sensitivities and specificities are quite different as such that sensitivity increases with decreasing specificity. Additionally, the model is used to construct componentwise sROC curves and to classify individual studies. The proposed method offers an alternative approach to model between-study heterogeneity in a diagnostic meta-analysis. Furthermore, it is possible to construct sROC curves even if a positive correlation between sensitivity and specificity is present. Copyright © 2015 Elsevier Inc. All rights reserved.

Groups graded by root systems and property (T)

PubMed Central

Ershov, Mikhail; Jaikin-Zapirain, Andrei; Kassabov, Martin; Zhang, Zezhou

2014-01-01

We establish property (T) for a large class of groups graded by root systems, including elementary Chevalley groups and Steinberg groups of rank at least 2 over finitely generated commutative rings with 1. We also construct a group with property (T) which surjects onto all finite simple groups of Lie type and rank at least two. PMID:25425669

Nonlinear Control Systems

DTIC Science & Technology

2007-03-01

Finite -dimensional regulators for a class of infinite dimensional systems ,” Systems and Control Letters, 3 (1983), 7-12. [11] B...semiglobal stabilizability by encoded state feedback,” to appear in Systems and Control Letters. 22 29. C. De Persis, A. Isidori, “Global stabilization of...nonequilibrium setting, for both finite and infinite dimensional control systems . Our objectives for distributed parameter systems included

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Finite conformal quantum gravity and spacetime singularities

NASA Astrophysics Data System (ADS)

Modesto, Leonardo; Rachwał, Lesław

2017-12-01

We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

Nonlinear Control Systems

DTIC Science & Technology

2009-11-18

J.M. Schumacher, Finite -dimensional regulators for a class of infinite dimensional systems . Systems and Control Letters, 3 (1983), 7-12. [39J J.M...for the control of certain examples or system classes us- ing particular feedback design methods ([20, 21, 16, 17, 19, 18]). Still, the control of...long time existence and asymptotic behavior for certain examples or system classes using particular feedback design methods (see, e.g., [20, 21, 16, 17

Dynamic load balancing of applications

DOEpatents

Wheat, Stephen R.

1997-01-01

An application-level method for dynamically maintaining global load balance on a parallel computer, particularly on massively parallel MIMD computers. Global load balancing is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method supports a large class of finite element and finite difference based applications and provides an automatic element management system to which applications are easily integrated.

Accuracy of a class of concurrent algorithms for transient finite element analysis

NASA Technical Reports Server (NTRS)

Ortiz, Michael; Sotelino, Elisa D.; Nour-Omid, Bahram

1988-01-01

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

Biomechanical 3-Dimensional Finite Element Analysis of Obturator Protheses Retained with Zygomatic and Dental Implants in Maxillary Defects

PubMed Central

Akay, Canan; Yaluğ, Suat

2015-01-01

Background The objective of this study was to investigate the stress distribution in the bone around zygomatic and dental implants for 3 different implant-retained obturator prostheses designs in a Aramany class IV maxillary defect using 3-dimensional finite element analysis (FEA). Material\\Methods A 3-dimensional finite element model of an Aramany class IV defect was created. Three different implant-retained obturator prostheses were modeled: model 1 with 1 zygomatic implant and 1 dental implant, model 2 with 1 zygomatic implant and 2 dental implants, and model 3 with 2 zygomatic implants. Locator attachments were used as a superstructure. A 150-N load was applied 3 different ways. Qualitative analysis was based on the scale of maximum principal stress; values obtained through quantitative analysis are expressed in MPa. Results In all loading conditions, model 3 (when compared models 1 and 2) showed the lowest maximum principal stress value. Model 3 is the most appropirate reconstruction in Aramany class IV maxillary defects. Two zygomatic implants can reduce the stresses in model 3. The distribution of stresses on prostheses were more rational with the help of zygoma implants, which can distribute the stresses on each part of the maxilla. Conclusions Aramany class IV obturator prosthesis placement of 2 zygomatic implants in each side of the maxilla is more advantageous than placement of dental implants. In the non-defective side, increasing the number of dental implants is not as suitable as zygomatic implants. PMID:25714086

"MONSTROUS MOONSHINE" and Physics

NASA Astrophysics Data System (ADS)

Pushkin, A. V.

The report presents some results obtained by the author on the quantum gravitation theory. Algebraic structure of this theory proves to be related to the commutative nonassociative Griess algebra. The theory symmetry is the automorphism group of Griess algebra: "Monster" simple group. Knowledge of the theory symmetry allows to compute observed physical values in the `zero' approximation. The report presents such computed results for values {m_{p}}/{m_{c}} and α, for the latter the `zero' approximation accuracy, controlled by the theory, being one order of magnitude higher than the accuracy of modern measurements.

z -classes of isometries of the hyperbolic space

NASA Astrophysics Data System (ADS)

Gongopadhyay, Krishnendu; Kulkarni, Ravi S.

Let G be a group. Two elements x, y are said to be z -equivalent if their centralizers are conjugate in G . The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z -classes provides important information about the internal structure of the group; cf. J. Ramanujan Math. Soc. 22 (2007), 35-56, for the elaboration of this theme. Let I(H^n) denote the group of isometries of the hyperbolic n -space, and let I_o(H^n) be the identity component of I(H^n) . We show that the number of z -classes in I(H^n) is finite. We actually compute their number; cf. theorem 1.3. We interpret the finiteness of z -classes as accounting for the finiteness of ``dynamical types'' in I(H^n) . Along the way we also parametrize conjugacy classes. We mainly use the linear model of the hyperbolic space for this purpose. This description of parametrizing conjugacy classes appears to be new; cf. Academic Press, New York, 1974, 49-87 and Conformal geometry (Bonn, 1985/1986), 41-64, Aspects Math., E12, Vieweg, Braunschweig, 1988, for previous attempts. Ahlfors (Differential Geometry and Complex Analysis (Springer, 1985), 65-73) suggested the use of Clifford algebras to deal with higher dimensional hyperbolic geometry; cf. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27, Quasiconformal Mappings and Analysis (Springer, 1998), 109-139, Complex Variables Theory Appl. 15 (1990), 125-133, and Adv. Math. 101 (1993), 87-113. These works may be compared to the approach suggested in this paper. In dimensions 2 and 3 , by remarkable Lie-theoretic isomorphisms, I_o(H2) and I_o(H3) can be lifted to GL_o(2, R) , and GL(2, C) respectively. For orientation-reversing isometries there are some modifications of these liftings. Using these liftings, in the appendix A, we have introduced a single numerical invariant c(A) , to classify the elements of I(H2) and I(H3) , and explained the classical terminology. Using the ``Iwasawa decomposition'' of I_o(H^n) , it is possible to equip H^n with a group structure. In the appendix B, we visualize the stratification of the group H^n into its conjugacy and z -classes.

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

NASA Astrophysics Data System (ADS)

Lucini, B.; Patella, A.; Ramos, A.; Tantalo, N.

2016-02-01

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C⋆ boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C⋆ boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Dynamic load balancing of applications

DOEpatents

Wheat, S.R.

1997-05-13

An application-level method for dynamically maintaining global load balance on a parallel computer, particularly on massively parallel MIMD computers is disclosed. Global load balancing is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method supports a large class of finite element and finite difference based applications and provides an automatic element management system to which applications are easily integrated. 13 figs.

Arithmetic and Hyperbolic Structures in String Theory

NASA Astrophysics Data System (ADS)

Persson, Daniel

2010-01-01

This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of a spacelike singularity (the "BKL-limit"). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be described in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of the theory. Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are described by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by automorphic forms on the double quotient G(Z)G/K. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on non-holomorphic Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also show how these techniques can be applied to hypermultiplet moduli spaces in type II Calabi-Yau compactifications, and we provide a detailed analysis for the universal hypermultiplet.

Ghost-free, finite, fourth-order D = 3 gravity.

PubMed

Deser, S

2009-09-04

Canonical analysis of a recently proposed linear + quadratic curvature gravity model in D = 3 establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing D > 3 quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode's second-derivative nature forfeits finiteness.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Finite-time synchronization control of a class of memristor-based recurrent neural networks.

PubMed

Jiang, Minghui; Wang, Shuangtao; Mei, Jun; Shen, Yanjun

2015-03-01

This paper presents a global and local finite-time synchronization control law for memristor neural networks. By utilizing the drive-response concept, differential inclusions theory, and Lyapunov functional method, we establish several sufficient conditions for finite-time synchronization between the master and corresponding slave memristor-based neural network with the designed controller. In comparison with the existing results, the proposed stability conditions are new, and the obtained results extend some previous works on conventional recurrent neural networks. Two numerical examples are provided to illustrate the effective of the design method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

Estimation of population mean in the presence of measurement error and non response under stratified random sampling

PubMed Central

Shabbir, Javid

2018-01-01

In the present paper we propose an improved class of estimators in the presence of measurement error and non-response under stratified random sampling for estimating the finite population mean. The theoretical and numerical studies reveal that the proposed class of estimators performs better than other existing estimators. PMID:29401519

New Tools for Hybrid Systems

DTIC Science & Technology

2007-05-02

stability of a class of discrete event systems ", IEEE Transactions on Automatic Control , vol. 39, no. 2... stability , input/output stability , external stability and incremental input/output stability , as they apply to deterministic finite state machine systems ... class of systems , incremental 1/0 stability and external stability are equivalent notions, stronger than the notion of I/O stability . 15. SUBJECT

Development of an hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1993-01-01

The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exac, and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite-element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement.

Small covers of graph-associahedra and realization of cycles

NASA Astrophysics Data System (ADS)

Gaifullin, A. A.

2016-11-01

An oriented connected closed manifold M^n is called a URC-manifold if for any oriented connected closed manifold N^n of the same dimension there exists a nonzero-degree mapping of a finite-fold covering \\widehat{M}^n of M^n onto N^n. This condition is equivalent to the following: for any n-dimensional integral homology class of any topological space X, a multiple of it can be realized as the image of the fundamental class of a finite-fold covering \\widehat{M}^n of M^n under a continuous mapping f\\colon \\widehat{M}^n\\to X. In 2007 the author gave a constructive proof of Thom's classical result that a multiple of any integral homology class can be realized as an image of the fundamental class of an oriented smooth manifold. This construction yields the existence of URC-manifolds of all dimensions. For an important class of manifolds, the so-called small covers of graph-associahedra corresponding to connected graphs, we prove that either they or their two-fold orientation coverings are URC-manifolds. In particular, we obtain that the two-fold covering of the small cover of the usual Stasheff associahedron is a URC-manifold. In dimensions 4 and higher, this manifold is simpler than all the previously known URC-manifolds. Bibliography: 39 titles.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

PubMed

Casey, M

1996-08-15

Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attractor structure of such systems is given. This knowledge effectively predicts activation space dynamics, which allows one to understand RNN computation dynamics in spite of complexity in activation dynamics. This theory provides a theoretical framework for understanding finite state machine (FSM) extraction techniques and can be used to improve training methods for RNNs performing FSM computations. This provides an example of a successful approach to understanding a general class of complex systems that has not been explicitly designed, e.g., systems that have evolved or learned their internal structure.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate.

PubMed

Gao, Lijun; Jiang, Xiaoxiao; Wang, Dandan

2016-03-01

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamics in the Decompositions Approach to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Harding, John

2017-12-01

In Harding (Trans. Amer. Math. Soc. 348(5), 1839-1862 1996) it was shown that the direct product decompositions of any non-empty set, group, vector space, and topological space X form an orthomodular poset Fact X. This is the basis for a line of study in foundational quantum mechanics replacing Hilbert spaces with other types of structures. Here we develop dynamics and an abstract version of a time independent Schrödinger's equation in the setting of decompositions by considering representations of the group of real numbers in the automorphism group of the orthomodular poset Fact X of decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwasniewski, Bartosz K

The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of themore » circle. Bibliography: 34 titles.« less

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

NASA Technical Reports Server (NTRS)

Sadovsky, Alexander V.; Davis, Damek; Isaacson, Douglas R.

2012-01-01

A class of problems in air traffic management asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures, but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs, hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the Fully Routed Nominal Problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively finite, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

Stability and Convergence of Underintegrated Finite Element Approximations

NASA Technical Reports Server (NTRS)

Oden, J. T.

1984-01-01

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Finite-time synchronization for memristor-based neural networks with time-varying delays.

PubMed

Abdurahman, Abdujelil; Jiang, Haijun; Teng, Zhidong

2015-09-01

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

NASA Astrophysics Data System (ADS)

Moraleda, Joaquín; Segurado, Javier; LLorca, Javier

2009-09-01

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

Effects of a finite outer scale on the measurement of atmospheric-turbulence statistics with a Hartmann wave-front sensor.

PubMed

Feng, Shen; Wenhan, Jiang

2002-06-10

Phase-structure and aperture-averaged slope-correlated functions with a finite outer scale are derived based on the Taylor hypothesis and a generalized spectrum, such as the von Kármán modal. The effects of the finite outer scale on measuring and determining the character of atmospheric-turbulence statistics are shown especially for an approximately 4-m class telescope and subaperture. The phase structure function and atmospheric coherent length based on the Kolmogorov model are approximations of the formalism we have derived. The analysis shows that it cannot be determined whether the deviation from the power-law parameter of Kolmogorov turbulence is caused by real variations of the spectrum or by the effect of the finite outer scale.

On cell entropy inequality for discontinuous Galerkin methods

NASA Technical Reports Server (NTRS)

Jiang, Guangshan; Shu, Chi-Wang

1993-01-01

We prove a cell entropy inequality for a class of high order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one dimensional scalar convex case.

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1987-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Assessment of agronomic homogeneity and compatibility of soils in the Vladimir Opolie region

NASA Astrophysics Data System (ADS)

Shein, E. V.; Kiryushin, V. I.; Korchagin, A. A.; Mazirov, M. A.; Dembovetskii, A. V.; Il'in, L. I.

2017-10-01

Complexes of gray forest soils of different podzolization degrees with the participation of gray forest podzolized soils with the second humus horizon play a noticeable role in the soil cover patterns of Vladimir Opolie. The agronomic homogeneity and agronomic compatibility of gray forest soils in automorphic positions ("plakor" sites) were assessed on the test field of the Vladimir Agricultural Research Institute. The term "soil homogeneity" implies in our study the closeness of crop yield estimates (scores) for the soil polygons; the term "soil compatibility" implies the possibility to apply the same technologies in the same dates for different soil polygons within a field. To assess the agronomic homogeneity and compatibility of soils, the statistical analysis of the yields of test crop (oats) was performed, and the spatial distribution of the particular parameters of soil hydrothermic regime was studied. The analysis of crop yields showed their high variability: the gray forest soils on microhighs showed the minimal potential fertility, and the maximal fertility was typical of the soils with the second humus horizon in microlows. Soils also differed significantly in their hydrothermic regime, as the gray forest soils with the second humus horizon were heated and cooled slower than the background gray forest soils; their temperature had a stronger lag effect and displayed a narrower amplitude in seasonal fluctuations; and these soils were wetter during the first weeks (40 days) of the growing season. Being colder and wetter, the soils with the second humus horizons reached their physical ripeness later than the gray forest soils. Thus, the soil cover of the test plot in the automorphic position is heterogeneous; from the agronomic standpoint, its components are incompatible.

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation, deformation of a cantilever bracket, and Boycott effects). The applicability of the method is not limited to flow in porous media, but can also be employed to describe many other physical systems governed by a similar set of equations, including e.g. multi-component materials.

Finite-time consensus for controlled dynamical systems in network

NASA Astrophysics Data System (ADS)

Zoghlami, Naim; Mlayeh, Rhouma; Beji, Lotfi; Abichou, Azgal

2018-04-01

The key challenges in networked dynamical systems are the component heterogeneities, nonlinearities, and the high dimension of the formulated vector of state variables. In this paper, the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift. For each model structure that defines homogeneous and heterogeneous multi-system behaviour, we derive protocols leading to finite-time consensus. For each model evolving in networks forming a homogeneous or heterogeneous multi-system, protocols integrating sufficient conditions are derived leading to finite-time consensus. Likewise, for the networking topology, we make use of fixed directed and undirected graphs. To prove our approaches, finite-time stability theory and Lyapunov methods are considered. As illustrative examples, the homogeneous multi-unicycle kinematics and the homogeneous/heterogeneous multi-second order dynamics in networks are studied.

Finite-time output feedback control of uncertain switched systems via sliding mode design

NASA Astrophysics Data System (ADS)

Zhao, Haijuan; Niu, Yugang; Song, Jun

2018-04-01

The problem of sliding mode control (SMC) is investigated for a class of uncertain switched systems subject to unmeasurable state and assigned finite (possible short) time constraint. A key issue is how to ensure the finite-time boundedness (FTB) of system state during reaching phase and sliding motion phase. To this end, a state observer is constructed to estimate the unmeasured states. And then, a state estimate-based SMC law is designed such that the state trajectories can be driven onto the specified integral sliding surface during the assigned finite time interval. By means of partitioning strategy, the corresponding FTB over reaching phase and sliding motion phase are guaranteed and the sufficient conditions are derived via average dwell time technique. Finally, an illustrative example is given to illustrate the proposed method.

On the asymptotic evolution of finite energy Airy wave functions.

PubMed

Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S

2015-06-15

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

LFSPMC: Linear feature selection program using the probability of misclassification

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.; Marion, B. P.

1975-01-01

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Computer-aided modeling and prediction of performance of the modified Lundell class of alternators in space station solar dynamic power systems

NASA Technical Reports Server (NTRS)

Demerdash, Nabeel A. O.; Wang, Ren-Hong

1988-01-01

The main purpose of this project is the development of computer-aided models for purposes of studying the effects of various design changes on the parameters and performance characteristics of the modified Lundell class of alternators (MLA) as components of a solar dynamic power system supplying electric energy needs in the forthcoming space station. Key to this modeling effort is the computation of magnetic field distribution in MLAs. Since the nature of the magnetic field is three-dimensional, the first step in the investigation was to apply the finite element method to discretize volume, using the tetrahedron as the basic 3-D element. Details of the stator 3-D finite element grid are given. A preliminary look at the early stage of a 3-D rotor grid is presented.

Periodic GMP Matrices

NASA Astrophysics Data System (ADS)

Eichinger, Benjamin

2016-07-01

We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic finite gap Jacobi matrices by periodic GMP matrices. Moreover, due to their structural similarity we can carry over numerous results from the direct and inverse spectral theory of periodic Jacobi matrices to the class of periodic GMP matrices. In particular, we prove an analogue of the remarkable ''magic formula'' for this new class.

Fast smooth second-order sliding mode control for systems with additive colored noises.

PubMed

Yang, Pengfei; Fang, Yangwang; Wu, Youli; Liu, Yunxia; Zhang, Danxu

2017-01-01

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

Scattering from finite bodies of translation - Plates, curved surfaces, and noncircular cylinders

NASA Astrophysics Data System (ADS)

Medgyesi-Mitschang, L. N.; Putnam, J. M.

1983-11-01

Electromagnetic scattering from finite, conducting bodies of translation (BOT) is examined using a formulation based on the electric field integral equation (EFIE) and solved by the method of moments (MM). The present approach provides a systematic, unified treatment for a wide class of finite, thin scatterers at all angles of illumination and polarization. Both concave and convex surfaces are considered. An entire-domain Galerkin expansion along one dimension of the body and a piecewise continuous one along the other are used to represent the unknown current variations. The scattering cross sections, obtained with this formulation, are compared with published results using more specialized methods and further confirmed by experimental measurements.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Iterative design of one- and two-dimensional FIR digital filters. [Finite duration Impulse Response

NASA Technical Reports Server (NTRS)

Suk, M.; Choi, K.; Algazi, V. R.

1976-01-01

The paper describes a new iterative technique for designing FIR (finite duration impulse response) digital filters using a frequency weighted least squares approximation. The technique is as easy to implement (via FFT) and as effective in two dimensions as in one dimension, and there are virtually no limitations on the class of filter frequency spectra approximated. An adaptive adjustment of the frequency weight to achieve other types of design approximation such as Chebyshev type design is discussed.

Application of the Group Foliation Method to the Complex Monge-Ampère Equation

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel, M. B.

2001-04-01

We apply the method of group foliation to the complex Monge-Ampère equation ( CMA 2) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup of CMA 2 to produce a foliation of the solution space into orbits of solutions with respect to this group and a corresponding splitting of CMA 2 into an automorphic system and a resolvent system. We propose a new approach to group foliation which is based on the commutator algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator representation of the resolvent system.

C*-algebras associated with reversible extensions of logistic maps

NASA Astrophysics Data System (ADS)

Kwaśniewski, Bartosz K.

2012-10-01

The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.

Construction of some hypergroups from combinatorial structures.

PubMed

Ashrafi, Ali Reza; Eslami-Harandi, Ahmad Reza

2003-01-01

Jajcay's studies (1993; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation [symbol: see text] on the group Syme(G), the stabilizer of the identity e [symbol: see text] G in the group Sym(G). We prove that (Syme(G), [symbol: see text]) is a hypergroup and characterize the subhypergroups of this hypergroup. Finally, we show that the set of all subhypergroups of Syme(G) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut(G).

Twisted sigma-model solitons on the quantum projective line

NASA Astrophysics Data System (ADS)

Landi, Giovanni

2018-04-01

On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather involved, the use of the positivity and the bound by the topological term lead to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit nontrivial solutions on the quantum projective line.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Effects of porosity distribution and porosity volume fraction on the electromechanical properties of 3-3 piezoelectric foams

NASA Astrophysics Data System (ADS)

Nguyen, B. V.; Challagulla, K. S.; Venkatesh, T. A.; Hadjiloizi, D. A.; Georgiades, A. V.

2016-12-01

Unit-cell based finite element models are developed to completely characterize the role of porosity distribution and porosity volume fraction in determining the elastic, dielectric and piezoelectric properties as well as relevant figures of merit of 3-3 type piezoelectric foam structures. Eight classes of foam structures which represent structures with different types and degrees of uniformity of porosity distribution are identified; a Base structure (Class I), two H-type foam structures (Classes II, and III), a Cross-type foam structure (Class IV) and four Line-type foam structures (Classes V, VI, VII, and VIII). Three geometric factors that influence the electromechanical properties are identified: (i) the number of pores per face, pore size and the distance between the pores; (ii) pore orientation with respect to poling direction; (iii) the overall symmetry of the pore distribution with respect to the center of the face of the unit cell. To assess the suitability of these structures for such applications as hydrophones, bone implants, medical imaging and diagnostic devices, five figures of merit are determined via the developed finite element model; the piezoelectric coupling constant (K t ), the acoustic impedance (Z), the piezoelectric charge coefficient (d h ), the hydrostatic voltage coefficient (g h ), and the hydrostatic figure of merit (d h g h ). At high material volume fractions, foams with non-uniform Line-type porosity (Classes V and VII) where the pores are preferentially distributed perpendicular to poling direction, are found to exhibit the best combination of desirable piezoelectric figures of merit. For example, at about 50% volume fraction, the d h , g h , and d h g h figures of merit are 55%, 1600% and 2500% higher, respectively, for Classes V and VII of Line-like foam structures compared with the Base structure.

On some methods of discrete systems behaviour simulation

NASA Astrophysics Data System (ADS)

Sytnik, Alexander A.; Posohina, Natalia I.

1998-07-01

The project is solving one of the fundamental problems of mathematical cybernetics and discrete mathematics, the one connected with synthesis and analysis of managing systems, depending on the research of their functional opportunities and reliable behaviour. This work deals with the case of finite-state machine behaviour restoration when the structural redundancy is not available and the direct updating of current behaviour is impossible. The described below method, uses number theory to build a special model of finite-state machine, it is simulating the transition between the states of the finite-state machine using specially defined functions of exponential type with the help of several methods of number theory and algebra it is easy to determine, whether there is an opportunity to restore the behaviour (with the help of this method) in the given case or not and also derive the class of finite-state machines, admitting such restoration.

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

Profinite Completions of Burnside-Type Quotients of Surface Groups

NASA Astrophysics Data System (ADS)

Funar, Louis; Lochak, Pierre

2018-06-01

Using quantum representations of mapping class groups, we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic quotients of surface groups.

Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.

PubMed

Douce, T; Markham, D; Kashefi, E; Diamanti, E; Coudreau, T; Milman, P; van Loock, P; Ferrini, G

2017-02-17

Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks

NASA Astrophysics Data System (ADS)

Lupo, Cosmo; Ottaviani, Carlo; Papanastasiou, Panagiotis; Pirandola, Stefano

2018-05-01

We present a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD) in a finite-size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after 107-109 quantum signal transmissions, depending on loss and noise, and on the required level of security.

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems.

PubMed

Han, Yaozhen; Liu, Xiangjie

2016-05-01

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

A class of cellular automata modeling winnerless competition

NASA Astrophysics Data System (ADS)

Afraimovich, V.; Ordaz, F. C.; Urías, J.

2002-06-01

Neural units introduced by Rabinovich et al. ("Sensory coding with dynamically competitive networks," UCSD and CIT, February 1999) motivate a class of cellular automata (CA) where spatio-temporal encoding is feasible. The spatio-temporal information capacity of a CA is estimated by the information capacity of the attractor set, which happens to be finitely specified. Two-dimensional CA are studied in detail. An example is given for which the attractor is not a subshift.

From anomalies of finite symmetries to heterotic GUTs

NASA Astrophysics Data System (ADS)

Vaudrevange, Patrick K. S.

2017-11-01

We review the role of finite symmetries for particle physics with special emphasis on discrete anomalies and on their possible origin from extra dimensions. Then, we apply our knowledge on finite symmetries to the problematic proton decay operators of various mass-dimensions, focusing on ℤ4R , i.e. a special R-symmetry of order 4. We show that this ℤ4R symmetry can naturally originate from extra dimensions as a discrete remnant of higher-dimensional Lorentz symmetry. Finally, in order to obtain a unified picture from the heterotic string theory we discuss grand unified theories (GUTs) in extra dimensions compactified on ℤ2 × ℤ2 orbifolds and show how proton decay operators can be suppressed in a certain class of orbifolds.

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

NASA Astrophysics Data System (ADS)

Yang, Peng-fei; Fang, Yang-wang; Wu, You-li; Zhang, Dan-xu; Xu, Yang

2018-01-01

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein-Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Finite key analysis for symmetric attacks in quantum key distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias

2006-10-15

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found.more » We also study secret key rates for protocols using higher-dimensional quantum systems.« less

Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback.

PubMed

Gao, Fangzheng; Wu, Yuqiang; Zhang, Zhongcai

2015-11-01

This paper investigates the problem of finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. Comparing with the existing relevant literature, a distinguishing feature of the systems under investigation is that the x-subsystem is a feedforward-like rather than feedback-like system. This renders the existing control methods inapplicable to the control problems of the systems. A constructive design procedure for output feedback control is given. The designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two simulation examples are provided to illustrate the effectiveness of the proposed approach. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Finite Element Modeling of the Deformation of a Thin Magnetoelastic Film Compared to a Membrane Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barham, M; White, D; Steigmann, D

2009-04-08

Recently a new class of biocompatible elastic polymers loaded with small ferrous particles (magnetoelastomer) was developed at Lawrence Livermore National Laboratory. This new material was formed as a thin film using spin casting. The deformation of this material using a magnetic field has many possible applications to microfluidics. Two methods will be used to calculate the deformation of a circular magneto-elastomeric film subjected to a magnetic field. The first method is an arbitrary Lagrangian-Eulerian (ALE) finite element method (FEM) and the second is based on nonlinear continuum electromagnetism and continuum elasticity in the membrane limit. The comparison of these twomore » methods is used to test/validate the finite element method.« less

Calculative techniques for transonic flows about certain classes of wing-body combinations, phase 2

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Spreiter, J. R.

1972-01-01

Theoretical analysis and associated computer programs were developed for predicting properties of transonic flows about certain classes of wing-body combinations. The procedures used are based on the transonic equivalence rule and employ either an arbitrarily-specified solution or the local linerization method for determining the nonlifting transonic flow about the equivalent body. The class of wind planform shapes include wings having sweptback trailing edges and finite tip chord. Theoretical results are presented for surface and flow-field pressure distributions for both nonlifting and lifting situations at Mach number one.

Evaluation of an improved finite-element thermal stress calculation technique

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1982-01-01

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

Mechanical topological insulator in zero dimensions

NASA Astrophysics Data System (ADS)

Lera, Natalia; Alvarez, J. V.

2018-04-01

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant Z2.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form < H^{α } f , g > for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

A finite-difference time-domain electromagnetic solver in a generalized coordinate system

NASA Astrophysics Data System (ADS)

Hochberg, Timothy Allen

A new, finite-difference, time-domain method for the simulation of full-wave electromagnetic wave propogation in complex structures is developed. This method is simple and flexible; it allows for the simulation of transient wave propogation in a large class of practical structures. Boundary conditions are implemented for perfect and imperfect electrically conducting boundaries, perfect magnetically conducting boundaries, and absorbing boundaries. The method is validated with the aid of several different types of test cases. Two types of coaxial cables with helical breaks are simulated and the results are discussed.

Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

NASA Astrophysics Data System (ADS)

Siudzińska, Katarzyna; Chruściński, Dariusz

2018-03-01

In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

NASA Astrophysics Data System (ADS)

Xu, Runzhang; Wang, Xingchang; Yang, Yanbing; Chen, Shaohua

2018-06-01

In this paper, we study the initial boundary value problem and global well-posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term, which was introduced to describe the dynamics of a suspension bridge. The global existence, decay estimate, and blow-up of solution at both subcritical (E(0) < d) and critical (E(0) = d) initial energy levels are obtained. Moreover, we prove the blow-up in finite time of solution at the supercritical initial energy level (E(0) > 0).

Expectation-maximization algorithms for learning a finite mixture of univariate survival time distributions from partially specified class values

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Youngrok

2013-05-15

Heterogeneity exists on a data set when samples from di erent classes are merged into the data set. Finite mixture models can be used to represent a survival time distribution on heterogeneous patient group by the proportions of each class and by the survival time distribution within each class as well. The heterogeneous data set cannot be explicitly decomposed to homogeneous subgroups unless all the samples are precisely labeled by their origin classes; such impossibility of decomposition is a barrier to overcome for estimating nite mixture models. The expectation-maximization (EM) algorithm has been used to obtain maximum likelihood estimates ofmore » nite mixture models by soft-decomposition of heterogeneous samples without labels for a subset or the entire set of data. In medical surveillance databases we can find partially labeled data, that is, while not completely unlabeled there is only imprecise information about class values. In this study we propose new EM algorithms that take advantages of using such partial labels, and thus incorporate more information than traditional EM algorithms. We particularly propose four variants of the EM algorithm named EM-OCML, EM-PCML, EM-HCML and EM-CPCML, each of which assumes a specific mechanism of missing class values. We conducted a simulation study on exponential survival trees with five classes and showed that the advantages of incorporating substantial amount of partially labeled data can be highly signi cant. We also showed model selection based on AIC values fairly works to select the best proposed algorithm on each specific data set. A case study on a real-world data set of gastric cancer provided by Surveillance, Epidemiology and End Results (SEER) program showed a superiority of EM-CPCML to not only the other proposed EM algorithms but also conventional supervised, unsupervised and semi-supervised learning algorithms.« less

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Adsorption of small hydrocarbon radicals on single walled carbon nanotubes of finite length

NASA Astrophysics Data System (ADS)

Wu, Jianhua; Hagelberg, Frank

2010-04-01

Adsorption of the hydrocarbon radicals CH, CH2 , and CH3 on finite single walled carbon nanotubes (SWNTs) of the (10,0) type is investigated by density-functional theory (DFT). Two classes of finite SWNTs are considered: truncated SWNTs, where admission is made for geometric reconstruction of the tube ends, and those capped with fullerene hemispheres. Both prototypes are characterized by ground states with nonvanishing magnetic moments, where antiferromagnetic coordination between nds is preferred over the ferromagnetic alternative. The focus of this study is on the influence exerted by the adsorbates on the magnetic structure of the system as a whole, as well as the relative impact of both, confinement due to the finite lengths of the considered SWNTs and their magnetic structure on the preferred positions of hydrocarbon adsorbates. In particular, it is shown that the confinement outweighs the magnetic effect in defining the adsorption energy variations among nonequivalent sites of attachment. The SWNT spin-density distributions turn out to affect the nature of the bonding between finite SWNT substrates and hydrocarbon radical adsorbates.

Coulomb branches with complex singularities

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Martone, Mario

2018-06-01

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.

Adinkras from ordered quartets of BC4 Coxeter group elements and regarding another Gadget’s 1,358,954,496 matrix elements

NASA Astrophysics Data System (ADS)

Gates, S. James; Kang, Lucas; Kessler, David S.; Korotkikh, Vadim

2018-04-01

A Gadget, more precisely a scalar Gadget, is defined as a mathematical calculation acting over a domain of one or more adinkra graphs and whose range is a real number. A 2010 work on the subject of automorphisms of adinkra graphs, implied the existence of multiple numbers of Gadgets depending on the number of colors under consideration. For four colors, this number is two. In this work, we verify the existence of a second such Gadget and calculate (both analytically and via explicit computer-enabled algorithms) its 1,358,954,496 matrix elements over 36,864 minimal valise adinkras related to the Coxeter Group BC4.

Regular black holes in f(T) Gravity through a nonlinear electrodynamics source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Junior, Ednaldo L.B.; Rodrigues, Manuel E.; Houndjo, Mahouton J.S., E-mail: ednaldobarrosjr@gmail.com, E-mail: esialg@gmail.com, E-mail: sthoundjo@yahoo.fr

2015-10-01

We seek to obtain a new class of exact solutions of regular black holes in f(T) Gravity with non-linear electrodynamics material content, with spherical symmetry in 4D. The equations of motion provide the regaining of various solutions of General Relativity, as a particular case where the function f(T)=T. We developed a powerful method for finding exact solutions, where we get the first new class of regular black holes solutions in the f(T) Theory, where all the geometrics scalars disappear at the origin of the radial coordinate and are finite everywhere, as well as a new class of singular black holes.

Extended symmetry analysis of generalized Burgers equations

NASA Astrophysics Data System (ADS)

Pocheketa, Oleksandr A.; Popovych, Roman O.

2017-10-01

Using enhanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form ut + uux + f(t, x)uxx = 0. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, hidden symmetries, conservation laws, potential admissible transformations, and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

Phase ordering in disordered and inhomogeneous systems

NASA Astrophysics Data System (ADS)

Corberi, Federico; Zannetti, Marco; Lippiello, Eugenio; Burioni, Raffaella; Vezzani, Alessandro

2015-06-01

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

This paper focuses on a class of generalized Ginzburg-Landau equations with random switching. In our formulation, the nonlinear term is allowed to have higher polynomial growth rate than the usual cubic polynomials. The random switching is modeled by a continuous-time Markov chain with a finite state space. First, an explicit solution is obtained. Then properties such as stochastic-ultimate boundedness and permanence of the solution processes are investigated. Finally, two-time-scale models are examined leading to a reduction of complexity.

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

Global Existence Results for Viscoplasticity at Finite Strain

NASA Astrophysics Data System (ADS)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-01-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Astrophysics Data System (ADS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1987-01-01

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien; Volin, Dmytro

2015-09-01

We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

Finite-time braiding exponents

NASA Astrophysics Data System (ADS)

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Finite-time braiding exponents.

PubMed

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Evaluating Mixture Modeling for Clustering: Recommendations and Cautions

ERIC Educational Resources Information Center

Steinley, Douglas; Brusco, Michael J.

2011-01-01

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison,…

Regular Gleason Measures and Generalized Effect Algebras

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij; Janda, Jiří

2015-12-01

We study measures, finitely additive measures, regular measures, and σ-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be studied in the frame of generalized effect algebras.

Nonparametric Transfer Function Models

PubMed Central

Liu, Jun M.; Chen, Rong; Yao, Qiwei

2009-01-01

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Nordstrom, Jan; Gottlieb, David

2007-01-01

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

Cooperative combinatorial optimization: evolutionary computation case study.

PubMed

Burgin, Mark; Eberbach, Eugene

2008-01-01

This paper presents a formalization of the notion of cooperation and competition of multiple systems that work toward a common optimization goal of the population using evolutionary computation techniques. It is proved that evolutionary algorithms are more expressive than conventional recursive algorithms, such as Turing machines. Three classes of evolutionary computations are introduced and studied: bounded finite, unbounded finite, and infinite computations. Universal evolutionary algorithms are constructed. Such properties of evolutionary algorithms as completeness, optimality, and search decidability are examined. A natural extension of evolutionary Turing machine (ETM) model is proposed to properly reflect phenomena of cooperation and competition in the whole population.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Crash Simulation of a Vertical Drop Test of a Commuter-Class Aircraft

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.

2004-01-01

A finite element model of an ATR42-300 commuter-class aircraft was developed and a crash simulation was executed. Analytical predictions were correlated with data obtained from a 30-ft/s (9.14-m/s) vertical drop test of the aircraft. The purpose of the test was to evaluate the structural response of the aircraft when subjected to a severe, but survivable, impact. The aircraft was configured with seats, dummies, luggage, and other ballast. The wings were filled with 8,700 lb. (3,946 kg) of water to represent the fuel. The finite element model, which consisted of 57,643 nodes and 62,979 elements, was developed from direct measurements of the airframe geometry. The seats, dummies, luggage, fuel, and other ballast were represented using concentrated masses. The model was executed in LS-DYNA, a commercial code for performing explicit transient dynamic simulations. Predictions of structural deformation and selected time-history responses were generated. The simulation was successfully validated through extensive test-analysis correlation.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Listing triangles in expected linear time on a class of power law graphs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann

Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysismore » for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.« less

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

On One-Dimensional Stretching Functions for Finite-Difference Calculations

NASA Technical Reports Server (NTRS)

Vinokur, M.

1980-01-01

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

Finite-time synchronization of fractional-order memristor-based neural networks with time delays.

PubMed

Velmurugan, G; Rakkiyappan, R; Cao, Jinde

2016-01-01

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Energy stable and high-order-accurate finite difference methods on staggered grids

NASA Astrophysics Data System (ADS)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Hierarchy of Certain Types of DNA Splicing Systems

NASA Astrophysics Data System (ADS)

Yusof, Yuhani; Sarmin, Nor Haniza; Goode, T. Elizabeth; Mahmud, Mazri; Heng, Fong Wan

A Head splicing system (H-system)consists of a finite set of strings (words) written over a finite alphabet, along with a finite set of rules that acts on the strings by iterated cutting and pasting to create a splicing language. Any interpretation that is aligned with Tom Head's original idea is one in which the strings represent double-stranded deoxyribonucleic acid (dsDNA) and the rules represent the cutting and pasting action of restriction enzymes and ligase, respectively. A new way of writing the rule sets is adopted so as to make the biological interpretation transparent. This approach is used in a formal language- theoretic analysis of the hierarchy of certain classes of splicing systems, namely simple, semi-simple and semi-null splicing systems. The relations between such systems and their associated languages are given as theorems, corollaries and counterexamples.

Generalized Wishart Mixtures for Unsupervised Classification of PolSAR Data

NASA Astrophysics Data System (ADS)

Li, Lan; Chen, Erxue; Li, Zengyuan

2013-01-01

This paper presents an unsupervised clustering algorithm based upon the expectation maximization (EM) algorithm for finite mixture modelling, using the complex wishart probability density function (PDF) for the probabilities. The mixture model enables to consider heterogeneous thematic classes which could not be better fitted by the unimodal wishart distribution. In order to make it fast and robust to calculate, we use the recently proposed generalized gamma distribution (GΓD) for the single polarization intensity data to make the initial partition. Then we use the wishart probability density function for the corresponding sample covariance matrix to calculate the posterior class probabilities for each pixel. The posterior class probabilities are used for the prior probability estimates of each class and weights for all class parameter updates. The proposed method is evaluated and compared with the wishart H-Alpha-A classification. Preliminary results show that the proposed method has better performance.

Double asymptotics for the chi-square statistic.

PubMed

Rempała, Grzegorz A; Wesołowski, Jacek

2016-12-01

Consider distributional limit of the Pearson chi-square statistic when the number of classes m n increases with the sample size n and [Formula: see text]. Under mild moment conditions, the limit is Gaussian for λ = ∞, Poisson for finite λ > 0, and degenerate for λ = 0.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Lecture Notes on Multigrid Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

Molecular symmetry with quaternions.

PubMed

Fritzer, H P

2001-09-01

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry.

On the vanishing couplings in ADE affine Toda field theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saitoh, Y.; Shimada, T.

In this paper, the authors show that certain vanishing couplins in the ADE affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. The authors develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. The authors shown that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance conditions plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in [bar A][sub n] affine Todamore » field theory is also proved in a standard massive scheme.« less

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

Regions of absolute ultimate boundedness for discrete-time systems.

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.

1972-01-01

This paper considers discrete-time systems of the Lur'e-Postnikov class where the linear part is not asymptotically stable and the nonlinear characteristic satisfies only partially the usual sector condition. Estimates of the resulting finite regions of absolute ultimate boundedness are calculated by means of a quadratic Liapunov function.

On the control canonical structure of a class of scalar input systems

NASA Technical Reports Server (NTRS)

Teglas, R.

1983-01-01

A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated.

Local Solutions in the Estimation of Growth Mixture Models

ERIC Educational Resources Information Center

Hipp, John R.; Bauer, Daniel J.

2006-01-01

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance

NASA Astrophysics Data System (ADS)

Rosestolato, M.; Święch, A.

2017-02-01

We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.

Evaluation of Measurement Instrument Criterion Validity in Finite Mixture Settings

ERIC Educational Resources Information Center

Raykov, Tenko; Marcoulides, George A.; Li, Tenglong

2016-01-01

A method for evaluating the validity of multicomponent measurement instruments in heterogeneous populations is discussed. The procedure can be used for point and interval estimation of criterion validity of linear composites in populations representing mixtures of an unknown number of latent classes. The approach permits also the evaluation of…

Finite-difference time-domain simulation of electromagnetic bandgap and bi-anisotropic metamaterials

NASA Astrophysics Data System (ADS)

Bray, Matthew G.

The term "Metamaterial" has been introduced into the electromagnetic lexicon in recent years to describe new artificial materials with electromagnetic properties that are not found in naturally occurring materials. Metamaterials exhibit electromagnetic properties that are not observed in its constituent materials, and/or not observed in nature. This thesis will analyze two different classes of metamaterials through the use of the finite-difference time-domain (FDTD) technique. The first class of metamaterials are artificial magnetic conductors (AMC) which approximate the behavior of a perfect magnetic conductor (PMC) over a finite frequency range. The AMC metamaterials are created through the use of an electromagnetic bandgap (EBG) structure. A periodic FDTD code is used to simulate a full-wave model of the metallodielectric EBG structures. The AMCs developed with the aid of the FDTD tool are then used to create low-profile antenna systems consisting of a dipole antenna in close proximity to an AMC surface. Through the use of this FDTD tool, several original contributions were made to the electromagnetic community. These include the first dual-band independently tunable EBG AMC ground plane and the first linearly polarized single-band and dual-band tunable antenna/EBG systems. The second class of materials analyzed are bi-anisotropic metamaterials. Bi-anisotropic media are the largest class of linear media which is able to describe the macroscopic material properties of artificial dielectrics, artificial magnetics, artificial chiral materials, left-handed materials, and other composite materials. The dispersive properties of these materials can be approximated by the oscillator model. This model assumes a Lorentzian frequency profile for the permittivity and permeability and a Condon model for chirality. A new FDTD formulation is introduced which can simulate this type of bi-anisotropic media. This FDTD method incorporates the dispersive material properties through a Z-transform technique derived from the constitutive relations for bi-anisotropic media. This is the first FDTD formulation to be able to simulate dispersive chiral media on a single FDTD grid. This tool was also used to perform the first simulations of dispersive chiral frequency selective surfaces.

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Parametric instabilities of finite-amplitude, circularly polarized Alfven waves in an anisotropic plasma

NASA Technical Reports Server (NTRS)

Hamabata, Hiromitsu

1993-01-01

A class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfven-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

Finite-size scaling analysis in the two-photon Dicke model

NASA Astrophysics Data System (ADS)

Chen, Xiang-You; Zhang, Yu-Yu

2018-05-01

We perform a Schrieffer-Wolff transformation to the two-photon Dicke model by keeping the leading-order correction with a quartic term of the field, which is crucial for finite-size scaling analysis. Besides a spectral collapse as a consequence of two-photon interaction, the super-radiant phase transition is indicated by the vanishing of the excitation energy and the uniform atomic polarization. The scaling functions for the ground-state energy and the atomic pseudospin are derived analytically. The scaling exponents of the observables are the same as those in the standard Dicke model, indicating they are in the same universality class.

A Morphological Approach to the Modeling of the Cold Spray Process

NASA Astrophysics Data System (ADS)

Delloro, F.; Jeandin, M.; Jeulin, D.; Proudhon, H.; Faessel, M.; Bianchi, L.; Meillot, E.; Helfen, L.

2017-12-01

A coating buildup model was developed, the aim of which was simulating the microstructure of a tantalum coating cold sprayed onto a copper substrate. To do so, first was operated a fine characterization of the irregular tantalum powder in 3D, using x-ray microtomography and developing specific image analysis algorithms. Particles were grouped by shape in seven classes. Afterward, 3D finite element simulations of the impact of the previously observed particles were realized. To finish, a coating buildup model was developed, based on the results of finite element simulations of particle impact. In its first version, this model is limited to 2D.

Active invisibility cloaks in one dimension

NASA Astrophysics Data System (ADS)

Mostafazadeh, Ali

2015-06-01

We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential, v (x ) , unidirectionally reflectionless or invisible at a wave number, k0, of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of v (x ) . The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We discuss their utility in making v (x ) bidirectionally invisible at k0 and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Behcet A.; Carson, John M., III

2005-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Sanity check for NN bound states in lattice QCD with Lüscher's finite volume formula - Disclosing Symptoms of Fake Plateaux -

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Doi, Takumi; Iritani, Takumi

2018-03-01

The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher's finite volume formula [1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4-5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansions (EREs) in NPL2013 violate the physical pole condition. (iv) Their comment is partly based on new data and analysis different from the original ones. (v) Their new ERE does not satisfy the Lüscher's finite volume formula.

A new technique for simulating composite material

NASA Technical Reports Server (NTRS)

Volakis, John L.

1991-01-01

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Constructions for finite-state codes

NASA Technical Reports Server (NTRS)

Pollara, F.; Mceliece, R. J.; Abdel-Ghaffar, K.

1987-01-01

A class of codes called finite-state (FS) codes is defined and investigated. These codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived from known upper bounds on the minimum distance of block codes. A general construction for FS codes is then given, based on the idea of partitioning a given linear block into cosets of one of its subcodes, and it is shown that in many cases the FS codes constructed in this way have a d sub free which is as large as possible. These codes are found without the need for lengthy computer searches, and have potential applications for future deep-space coding systems. The issue of catastropic error propagation (CEP) for FS codes is also investigated.

Probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates.

PubMed

Hebaz, Salah-Eddine; Benmeddour, Farouk; Moulin, Emmanuel; Assaad, Jamal

2018-01-01

The development of reliable guided waves inspection systems is conditioned by an accurate knowledge of their dispersive properties. The semi-analytical finite element method has been proven to be very practical for modeling wave propagation in arbitrary cross-section waveguides. However, when it comes to computations on complex geometries to a given accuracy, it still has a major drawback: the high consumption of resources. Recently, discontinuous Galerkin finite element method (DG-FEM) has been found advantageous over the standard finite element method when applied as well in the frequency domain. In this work, a high-order method for the computation of Lamb mode characteristics in plates is proposed. The problem is discretised using a class of DG-FEM, namely, the interior penalty methods family. The analytical validation is performed through the homogeneous isotropic case with traction-free boundary conditions. Afterwards, functionally graded material plates are analysed and a numerical example is presented. It was found that the obtained results are in good agreement with those found in the literature.

Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata

NASA Astrophysics Data System (ADS)

Young, Frederic; Siegel, Edward

Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

Finite burn maneuver modeling for a generalized spacecraft trajectory design and optimization system.

PubMed

Ocampo, Cesar

2004-05-01

The modeling, design, and optimization of finite burn maneuvers for a generalized trajectory design and optimization system is presented. A generalized trajectory design and optimization system is a system that uses a single unified framework that facilitates the modeling and optimization of complex spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The modeling and optimization issues associated with the use of controlled engine burn maneuvers of finite thrust magnitude and duration are presented in the context of designing and optimizing a wide class of finite thrust trajectories. Optimal control theory is used examine the optimization of these maneuvers in arbitrary force fields that are generally position, velocity, mass, and are time dependent. The associated numerical methods used to obtain these solutions involve either, the solution to a system of nonlinear equations, an explicit parameter optimization method, or a hybrid parameter optimization that combines certain aspects of both. The theoretical and numerical methods presented here have been implemented in copernicus, a prototype trajectory design and optimization system under development at the University of Texas at Austin.

Extremal higher spin black holes

NASA Astrophysics Data System (ADS)

Bañados, Máximo; Castro, Alejandra; Faraggi, Alberto; Jottar, Juan I.

2016-04-01

The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory. In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble. Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3 d higher spin theories. Our definition can be phrased in terms of the Jordan class of the holonomy around a non-contractible (angular) cycle, and we show that it is compatible with the zero-temperature limit of smooth black hole solutions. While this notion of extremality does not require supersymmetry, we exemplify its consequences in the context of sl(3|2) ⊕ sl(3|2) Chern-Simons theory and show that, as usual, not all extremal solutions preserve supersymmetries. Remarkably, we find in addition that the higher spin setup allows for non-extremal supersymmetric black hole solutions. Furthermore, we discuss our results from the perspective of the holographic duality between sl(3|2) ⊕ sl(3|2) Chern-Simons theory and two-dimensional CFTs with W (3|2) symmetry, the simplest higher spin extension of the N = 2 super-Virasoro algebra. In particular, we compute W (3|2) BPS bounds at the full quantum level, and relate their semiclassical limit to extremal black hole or conical defect solutions in the 3 d bulk. Along the way, we discuss the role of the spectral flow automorphism and provide a conjecture for the form of the semiclassical BPS bounds in general N = 2 two-dimensional CFTs with extended symmetry algebras.

Nonlinear Structured Growth Mixture Models in M"plus" and OpenMx

ERIC Educational Resources Information Center

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2010-01-01

Growth mixture models (GMMs; B. O. Muthen & Muthen, 2000; B. O. Muthen & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models…

Non-locality Sudden Death in Tripartite Systems

NASA Astrophysics Data System (ADS)

Jaeger, Gregg; Ann, Kevin

2009-03-01

Bell non-locality sudden death is the disappearance of non-local properties in finite times under local phase noise, which decoheres states only in the infinite-time limit. We consider the relationship between decoherence, disentanglement, and Bell non-locality sudden death in bipartite and tripartite systems in specific large classes of state preparation.

Generic tripartite Bell nonlocality sudden death under local phase noise

NASA Astrophysics Data System (ADS)

Ann, Kevin; Jaeger, Gregg

2008-11-01

We definitively show, using an explicit and broadly applicable model, that local phase noise that is capable of eliminating state coherence only in the infinite-time limit is capable of eliminating nonlocality in finite time in three two-level systems prepared in the Bell-nonlocal tripartite states of the generic entanglement class.

Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.; Kwon, K. H.

2001-07-01

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1,1).

On Classification of Modular Categories by Rank: Table A.1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruillard, Paul; Ng, Siu-Hung; Rowell, Eric C.

2016-04-10

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=5 modular categories and describe the corresponding monoidal equivalence classes.

On the entanglement entropy of quantum fields in causal sets

NASA Astrophysics Data System (ADS)

Belenchia, Alessio; Benincasa, Dionigi M. T.; Letizia, Marco; Liberati, Stefano

2018-04-01

In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2, 3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set’s retarded nonlocal d’Alembertians parametrised by a length scale l k . In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in Sorkin and Yazdi (2016 Entanglement entropy in causal set theory (arXiv:1611.10281)) is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for why these two cutoff are necessary, and the different roles they play in making the entanglement entropy on causal sets finite.

Extreme Quantum Memory Advantage for Rare-Event Sampling

NASA Astrophysics Data System (ADS)

Aghamohammadi, Cina; Loomis, Samuel P.; Mahoney, John R.; Crutchfield, James P.

2018-02-01

We introduce a quantum algorithm for memory-efficient biased sampling of rare events generated by classical memoryful stochastic processes. Two efficiency metrics are used to compare quantum and classical resources for rare-event sampling. For a fixed stochastic process, the first is the classical-to-quantum ratio of required memory. We show for two example processes that there exists an infinite number of rare-event classes for which the memory ratio for sampling is larger than r , for any large real number r . Then, for a sequence of processes each labeled by an integer size N , we compare how the classical and quantum required memories scale with N . In this setting, since both memories can diverge as N →∞ , the efficiency metric tracks how fast they diverge. An extreme quantum memory advantage exists when the classical memory diverges in the limit N →∞ , but the quantum memory has a finite bound. We then show that finite-state Markov processes and spin chains exhibit memory advantage for sampling of almost all of their rare-event classes.

Double-trace flows and the swampland

NASA Astrophysics Data System (ADS)

Giombi, Simone; Perlmutter, Eric

2018-03-01

We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k, deformed by \\int O^2, where O is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1 /N. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT3 with an Einstein gravity dual.

Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver

NASA Astrophysics Data System (ADS)

Alemi Ardakani, Hamid; Bridges, Thomas J.; Turner, Matthew R.

2016-06-01

A class of augmented approximate Riemann solvers due to George (2008) [12] is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

Transcutaneous RF-Powered Implantable Minipump Driven by a Class-E Transmitter

PubMed Central

Moore, William H.; Holschneider, Daniel P.; Givrad, Tina K.

2007-01-01

We describe the design and testing of an inductive coupling system used to power an implantable minipump for applications in ambulating rats. A 2 MHz class-E oscillator driver powered a coil transmitter wound around a 33-cm-diameter rat cage. A receiver coil, a filtered rectifier, and a voltage-sensitive switch powered the implant. The implant DC current at the center of the primary coil (5.1 V) exceeded the level required to activate the solenoid valve in the pump. The variations of the implant current in the volume of the primary coil reflected the variations of the estimated coupling coefficient between the two coils. The pump could be activated in-vivo, while accommodating the vertical and horizontal movements of the animal. Advantages of this design include a weight reduction for the implant, an operation independent from a finite power source, and a remote activation/deactivation. PMID:16916107

Transcutaneous RF-powered implantable minipump driven by a class-E transmitter.

PubMed

Moore, William H; Holschneider, Daniel P; Givrad, Tina K; Maarek, Jean-Michel I

2006-08-01

We describe the design and testing of an inductive coupling system used to power an implantable minipump for applications in ambulating rats. A 2 MHz class-E oscillator driver powered a coil transmitter wound around a 33-cm-diameter rat cage. A receiver coil, a filtered rectifier, and a voltage-sensitive switch powered the implant. The implant DC current at the center of the primary coil (5.1 V) exceeded the level required to activate the solenoid valve in the pump. The variations of the implant current in the volume of the primary coil reflected the variations of the estimated coupling coefficient between the two coils. The pump could be activated in-vivo, while accommodating the vertical and horizontal movements of the animal. Advantages of this design include a weight reduction for the implant, an operation independent from a finite power source, and a remote activation/deactivation.

Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening

PubMed Central

Pan, Rui; Wang, Hansheng; Li, Runze

2016-01-01

This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure independence screening method for linear discriminant analysis with an ultrahigh dimensional predictor. The proposed procedure is directly applicable to the situation with many classes. We further prove that the proposed method is screening consistent. Simulation studies are conducted to assess the finite sample performance of the new procedure. We also demonstrate the proposed methodology via an empirical analysis of a real life example on handwritten Chinese character recognition. PMID:28127109

Soil catenas on denudation plains in the forest-tundra and northern taiga zones of the Kola Peninsula

NASA Astrophysics Data System (ADS)

Urusevskaya, I. S.

2017-07-01

Morphogenetic features of soils of two catenas developed on sandy to loamy sandy moraine deposits in the forest-tundra and northern taiga zones on denudation plains of the Kola Peninsula are discussed. It is shown that these catenas are similar with respect to the major directions of soil formation, regularities of soil distribution by the elements of mesotopography, and the factors of the soil cover differentiation. The differences between the catenas are of quantitative character and are related to the intensities of manifestation of the particular processes and features. Both catenas are characterized by the pronounced differentiation of soils with respect to their moistening with hydromorphic peat bog soils in the subordinate positions and Al-Fe-humus podzols in the automorphic positions.

Two new constructions of approximately SIC-POVMs from multiplicative characters

NASA Astrophysics Data System (ADS)

Luo, Gaojun; Cao, Xiwang

2017-12-01

In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are relevant to quantum state tomography [8], quantum cryptography [15], and foundational studies [16]. In general, it is hard to construct SIC-POVMs and only a few classes of them existed, as we know. Moreover, we do not know whether there exists an infinite class of them. Many researchers tried to construct approximately symmetric informationally complete positive operator-valued measures (ASIC-POVMs). In this paper, we propose two new constructions of ASIC-POVMs for prime power dimensions only by using multiplicative characters over finite fields.

Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior?

NASA Astrophysics Data System (ADS)

Salerno, K. Michael; Maloney, Craig E.; Robbins, Mark O.

2012-09-01

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

Improved finite difference schemes for transonic potential calculations

NASA Technical Reports Server (NTRS)

Hafez, M.; Osher, S.; Whitlow, W., Jr.

1984-01-01

Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

Stochastic evolution in populations of ideas

PubMed Central

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244

High-order cyclo-difference techniques: An alternative to finite differences

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Otto, John C.

1993-01-01

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

A Simulation Study on Optimal Design Parameters of 200V Class Induction Range using Finite Element Method

NASA Astrophysics Data System (ADS)

Ohchi, Masashi; Furukawa, Tatsuya

Induction heating has found a new feasibility in domestic appliances. Its application is known as an “induction range” or an “induction heating oven”. Conventional design schemes of them have depended on the experience and insight of designers. In the paper, the authors treat it as an electromagnetic device to investigate the mechanism of power dissipation using the Finite Element Method, where an impressed voltage supply is taken account of and the constant V/f condition is imposed for the constant impressed magnetic flux. Furthermore the authors will examine how to heat an aluminum pan and discuss the optimal frequency of a power supply.

Simulation of CNT-AFM tip based on finite element analysis for targeted probe of the biological cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yousefi, Amin Termeh, E-mail: at.tyousefi@gmail.com; Miyake, Mikio, E-mail: miyakejaist@gmail.com; Ikeda, Shoichiro, E-mail: sho16.ikeda@gmail.com

Carbon nanotubes (CNTs) are potentially ideal tips for atomic force microscopy (AFM) due to the robust mechanical properties, nano scale diameter and also their ability to be functionalized by chemical and biological components at the tip ends. This contribution develops the idea of using CNTs as an AFM tip in computational analysis of the biological cell’s. Finite element analysis employed for each section and displacement of the nodes located in the contact area was monitored by using an output database (ODB). This reliable integration of CNT-AFM tip process provides a new class of high performance nanoprobes for single biological cellmore » analysis.« less

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

Stochastic evolution in populations of ideas

NASA Astrophysics Data System (ADS)

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christon, Mark A.; Bakosi, Jozsef; Lowrie, Robert B.

Hydra-TH is a hybrid finite-element/finite-volume code built using the Hydra toolkit specifically to attack a broad class of incompressible, viscous fluid dynamics problems prevalent in the thermalhydraulics community. The purpose for this manual is provide sufficient information for an experience analyst to use Hydra-TH in an effective way. The Hydra-TH User's Manual present a brief overview of capabilities and visualization interfaces. The execution and restart models are described before turning to the detailed description of keyword input. Finally, a series of example problems are presented with sufficient data to permit the user to verify the local installation of Hydra-TH, andmore » to permit a convenient starting point for more detailed and complex analyses.« less

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE PAGES

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

2017-02-05

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

The linear regulator problem for parabolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1983-01-01

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

A Class of Population Covariance Matrices in the Bootstrap Approach to Covariance Structure Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro; Yanagihara, Hirokazu

2007-01-01

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given…

Localization on Quantum Graphs with Random Vertex Couplings

NASA Astrophysics Data System (ADS)

Klopp, Frédéric; Pankrashkin, Konstantin

2008-05-01

We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges.

An approximation formula for a class of fault-tolerant computers

NASA Technical Reports Server (NTRS)

White, A. L.

1986-01-01

An approximation formula is derived for the probability of failure for fault-tolerant process-control computers. These computers use redundancy and reconfiguration to achieve high reliability. Finite-state Markov models capture the dynamic behavior of component failure and system recovery, and the approximation formula permits an estimation of system reliability by an easy examination of the model.

The infinum principle

NASA Technical Reports Server (NTRS)

Geering, H. P.; Athans, M.

1973-01-01

A complete theory of necessary and sufficient conditions is discussed for a control to be superior with respect to a nonscalar-valued performance criterion. The latter maps into a finite dimensional, integrally closed directed, partially ordered linear space. The applicability of the theory to the analysis of dynamic vector estimation problems and to a class of uncertain optimal control problems is demonstrated.

Multi-Class Analytical Models of the DECsystem-10 Job-Swapping Behavior.

DTIC Science & Technology

1981-12-01

Mark of the Unicorn for developing Scribble, the best text formatter for a CP/M home computer I’ve ever seen, and for their patient help when I...requests for service will tend to decrease as the queue length grows . The finite population model, also known as the machine interference model, was

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations.

PubMed

Lv, Jian-Ping; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D

2018-04-01

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c=1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

NASA Astrophysics Data System (ADS)

Lv, Jian-Ping; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.

2018-04-01

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c =1 . The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part 1; Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2009-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

Positivity, discontinuity, finite resources, and nonzero error for arbitrarily varying quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boche, H., E-mail: boche@tum.de, E-mail: janis.noetzel@tum.de; Nötzel, J., E-mail: boche@tum.de, E-mail: janis.noetzel@tum.de

2014-12-15

This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuousmore » in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.« less

Finite-Horizon $H_\\infty $ Consensus for Multiagent Systems With Redundant Channels via An Observer-Type Event-Triggered Scheme.

PubMed

Xu, Wenying; Wang, Zidong; Ho, Daniel W C

2018-05-01

This paper is concerned with the finite-horizon consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.

Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

Position-dependent mass, finite-gap systems, and supersymmetry

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Plyushchay, Mikhail S.

2016-05-01

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first-order supercharges from the kinetic term alone, while inclusion of the potential term allows us also to generate nonlinear supersymmetry with higher-order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lamé and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS2 -related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Logical definability and asymptotic growth in optimization and counting problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Compton, K.

1994-12-31

There has recently been a great deal of interest in the relationship between logical definability and NP-optimization problems. Let MS{sub n} (resp. MP{sub n}) be the class of problems to compute, for given a finite structure A, the maximum number of tuples {bar x} in A satisfying a {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar x}, {bar S}) as {bar S} ranges over predicates on A. Kolaitis and Thakur showed that the classes MS{sub n} and MP{sub n} collapse to a hierarchy of four levels. Papadimitriou and Yannakakis previously showed that problems in the two lowest levels MS{sub 0} andmore » MS{sub 1} (which they called Max Snp and Max Np) are approximable to within a contrast factor in polynomial time. Similarly, Saluja, Subrahmanyam, and Thakur defined SS{sub n} (resp. SP{sub n}) to be the class of problems to compute, for given a finite structure A, the number of tuples ({bar T}, {bar S}) satisfying a given {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar T}, {bar c}) in A. They showed that the classes SS{sub n} and SP{sub n} collapse to a hierarchy of five levels and that problems in the two lowest levels SS{sub 0} and SS{sub 1} have a fully polynomial time randomized approximation scheme. We define extended classes MSF{sub n}, MPF{sub n} SSF{sub n}, and SPF{sub n} by allowing formulae to contain predicates definable in a logic known as least fixpoint logic. The resulting hierarchies classes collapse to the same number of levels and problems in the bottom levels can be approximated as before, but now some problems descend from the highest levels in the original hierarchies to the lowest levels in the new hierarchies. We introduce a method characterizing rates of growth of average solution sizes thereby showing a number of important problems do not belong MSF{sub 1} and SSF{sub 1}. This method is related to limit laws for logics and the probabilistic method from combinatorics.« less

ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS

PubMed Central

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-01-01

The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks. PMID:27761104

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

Design of sliding-mode observer for a class of uncertain neutral stochastic systems

NASA Astrophysics Data System (ADS)

Liu, Zhen; Zhao, Lin; Zhu, Quanmin; Gao, Cunchen

2017-05-01

The problem of robust ? control for a class of uncertain neutral stochastic systems (NSS) is investigated by utilising the sliding-mode observer (SMO) technique. This paper presents a novel observer and integral-type sliding-surface design, based on which a new sufficient condition guaranteeing the resultant sliding-mode dynamics (SMDs) to be mean-square exponentially stable with a prescribed level of ? performance is derived. Then, an adaptive reaching motion controller is synthesised to lead the system to the predesigned sliding surface in finite-time almost surely. Finally, two illustrative examples are exhibited to verify the validity and superiority of the developed scheme.

Experimental test of nonlocal realistic theories without the rotational symmetry assumption.

PubMed

Paterek, Tomasz; Fedrizzi, Alessandro; Gröblacher, Simon; Jennewein, Thomas; Zukowski, Marek; Aspelmeyer, Markus; Zeilinger, Anton

2007-11-23

We analyze the class of nonlocal realistic theories that was originally considered by Leggett [Found. Phys. 33, 1469 (2003)10.1023/A:1026096313729] and tested by us in a recent experiment [Nature (London) 446, 871 (2007)10.1038/nature05677]. We derive an incompatibility theorem that works for finite numbers of polarizer settings and that does not require the previously assumed rotational symmetry of the two-particle correlation functions. The experimentally measured case involves seven different measurement settings. Using polarization-entangled photon pairs, we exclude this broader class of nonlocal realistic models by experimentally violating a new Leggett-type inequality by 80 standard deviations.

Reducing Neuronal Networks to Discrete Dynamics

PubMed Central

Terman, David; Ahn, Sungwoo; Wang, Xueying; Just, Winfried

2008-01-01

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [1], we analyze the discrete model. PMID:18443649

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Near-optimal, asymptotic tracking in control problems involving state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Markopoulos, N.; Calise, A. J.

1993-01-01

The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.

On the stability of a class of isothermal, magnetostatic atmospheres. [in sun

NASA Technical Reports Server (NTRS)

Webb, G. M.; Ko, C. M.

1989-01-01

The stability of a class of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is explored. Special attention is given to the stability of nonpotential equilibria that have the same magnetic field geometry as the potential equilibrium of the solution family. It is found that equilibria in which the source currents for the potential field are buried at large distances below the photospheric base are stable. Also considered is the stability of configurations in which the source currents for the potential field are located at a finite depth below the base.

Global existence and finite time blow-up for a class of thin-film equation

NASA Astrophysics Data System (ADS)

Dong, Zhihua; Zhou, Jun

2017-08-01

This paper deals with a class of thin-film equation, which was considered in Li et al. (Nonlinear Anal Theory Methods Appl 147:96-109, 2016), where the case of lower initial energy (J(u_0)≤ d and d is a positive constant) was discussed, and the conditions on global existence or blow-up are given. We extend the results of this paper on two aspects: Firstly, we consider the upper and lower bounds of blow-up time and asymptotic behavior when J(u_0)d.

Unidirectional spectral singularities.

PubMed

Ramezani, Hamidreza; Li, Hao-Kun; Wang, Yuan; Zhang, Xiang

2014-12-31

We propose a class of spectral singularities emerging from the coincidence of two independent singularities with highly directional responses. These spectral singularities result from resonance trapping induced by the interplay between parity-time symmetry and Fano resonances. At these singularities, while the system is reciprocal in terms of a finite transmission, a simultaneous infinite reflection from one side and zero reflection from the opposite side can be realized.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

Improving the Lieb-Robinson Bound for Long-Range Interactions

NASA Astrophysics Data System (ADS)

Matsuta, Takuro; Koma, Tohru; Nakamura, Shu

2017-02-01

We improve the Lieb-Robinson bound for a wide class of quantum many-body systems with long-range interactions decaying by power law. As an application, we show that the group velocity of information propagation grows by power law in time for such systems, whereas systems with short-range interactions exhibit a finite group velocity as shown by Lieb and Robinson.

Killing spinors are Killing vector fields in Riemannian supergeometry

NASA Astrophysics Data System (ADS)

Alekseevsky, D. V.; Cortés, V.; Devchand, C.; Semmelmann, U.

1998-06-01

A supermanifold M is canonically associated to any pseudo-Riemannian spin manifold ( M0, g0). Extending the metric g0 to a field g of bilinear forms g( p) on TpM, pɛM0, the pseudo-Riemannian supergeometry of ( M, g) is formulated as G-structure on M, where G is a supergroup with even part G 0 ≊ Spin(k, l); (k, l) the signature of ( M0, go). Killing vector fields on ( M, g) are, by definition, infinitesimal automorphisms of this G-structure. For every spinor field s there exists a corresponding odd vector field Xs on M. Our main result is that Xs is a Killing vector field on ( M, g) if and only if s is a twistor spinor. In particular, any Killing spinor s defines a Killing vector field Xs.

Eisenstein type series for Calabi-Yau varieties

NASA Astrophysics Data System (ADS)

Movasati, Hossein

2011-06-01

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi-Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.

Symmetries and Invariants of Twisted Quantum Algebras and Associated Poisson Algebras

NASA Astrophysics Data System (ADS)

Molev, A. I.; Ragoucy, E.

We construct an action of the braid group BN on the twisted quantized enveloping algebra U q'( {o}N) where the elements of BN act as automorphisms. In the classical limit q → 1, we recover the action of BN on the polynomial functions on the space of upper triangular matrices with ones on the diagonal. The action preserves the Poisson bracket on the space of polynomials which was introduced by Nelson and Regge in their study of quantum gravity and rediscovered in the mathematical literature. Furthermore, we construct a Poisson bracket on the space of polynomials associated with another twisted quantized enveloping algebra U q'( {sp}2n). We use the Casimir elements of both twisted quantized enveloping algebras to reproduce and construct some well-known and new polynomial invariants of the corresponding Poisson algebras.

A generalized volumetric dispersion model for a class of two-phase separation/reaction: finite difference solutions

NASA Astrophysics Data System (ADS)

Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut

2017-03-01

This article explores a volumetric approach in formulating differential equations for a class of engineering flow problems involving component transfer within or between two phases. In contrast to conventional formulation which is based on linear velocities, this work proposed a slightly different approach based on volumetric flow-rate which is essentially constant in many industrial processes. In effect, many multi-dimensional flow problems found industrially can be simplified into multi-component or multi-phase but one-dimensional flow problems. The formulation is largely generic, covering counter-current, concurrent or batch, fixed and fluidized bed arrangement. It was also intended to use for start-up, shut-down, control and steady state simulation. Since many realistic and industrial operation are dynamic with variable velocity and porosity in relation to position, analytical solutions are rare and limited to only very simple cases. Thus we also provide a numerical solution using Crank-Nicolson finite difference scheme. This solution is inherently stable as tested against a few cases published in the literature. However, it is anticipated that, for unconfined flow or non-constant flow-rate, traditional formulation should be applied.

The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable

NASA Astrophysics Data System (ADS)

Bochicchio, Marco

2017-03-01

Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

Some calculable contributions to entanglement entropy.

PubMed

Hertzberg, Mark P; Wilczek, Frank

2011-02-04

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry: its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.

A fourth order accurate finite difference scheme for the computation of elastic waves

NASA Technical Reports Server (NTRS)

Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

1986-01-01

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Complex networks: Effect of subtle changes in nature of randomness

NASA Astrophysics Data System (ADS)

Goswami, Sanchari; Biswas, Soham; Sen, Parongama

2011-03-01

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain the same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

NASA Astrophysics Data System (ADS)

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α , the appropriate FRCG model has the effective range d =b2/N =α2/N , for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

NASA Astrophysics Data System (ADS)

de Oliveira, M. M.; da Luz, M. G. E.; Fiore, C. E.

2015-12-01

Based on quasistationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as response functions, cumulants, and equal area probability distributions all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions—to single and infinitely many absorbing states—are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasistationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to a unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Nonlinear analysis of structures. [within framework of finite element method

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.

1974-01-01

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.

Modeling of a reinforced concrete beam using shape memory alloy as reinforcement bars

NASA Astrophysics Data System (ADS)

Bajoria, Kamal M.; Kaduskar, Shreya S.

2017-04-01

In this paper the structural behavior of reinforced concrete (RC) beams with smart rebars under three point loading system has been numerically studied, using Finite Element Method. The material used in this study is Superelastic Shape Memory Alloy (SE SMA) which contains nickel and titanium. Shape memory alloys (SMAs) are a unique class of materials which have ability to undergo large deformation and also regain their un-deformed shape by removal of stress or by heating. In this study, a uniaxial SMA model is able to reproduce the pseudo-elastic behavior for the reinforcing SMA wires. Finite element simulation is developed in order to study the load-deflection behavior of smart concrete beams subjected to three-point bending tests.

Parallel Three-Dimensional Computation of Fluid Dynamics and Fluid-Structure Interactions of Ram-Air Parachutes

NASA Technical Reports Server (NTRS)

Tezduyar, Tayfun E.

1998-01-01

This is a final report as far as our work at University of Minnesota is concerned. The report describes our research progress and accomplishments in development of high performance computing methods and tools for 3D finite element computation of aerodynamic characteristics and fluid-structure interactions (FSI) arising in airdrop systems, namely ram-air parachutes and round parachutes. This class of simulations involves complex geometries, flexible structural components, deforming fluid domains, and unsteady flow patterns. The key components of our simulation toolkit are a stabilized finite element flow solver, a nonlinear structural dynamics solver, an automatic mesh moving scheme, and an interface between the fluid and structural solvers; all of these have been developed within a parallel message-passing paradigm.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

PubMed

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

1985-01-01

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

Learning Extended Finite State Machines

NASA Technical Reports Server (NTRS)

Cassel, Sofia; Howar, Falk; Jonsson, Bengt; Steffen, Bernhard

2014-01-01

We present an active learning algorithm for inferring extended finite state machines (EFSM)s, combining data flow and control behavior. Key to our learning technique is a novel learning model based on so-called tree queries. The learning algorithm uses the tree queries to infer symbolic data constraints on parameters, e.g., sequence numbers, time stamps, identifiers, or even simple arithmetic. We describe sufficient conditions for the properties that the symbolic constraints provided by a tree query in general must have to be usable in our learning model. We have evaluated our algorithm in a black-box scenario, where tree queries are realized through (black-box) testing. Our case studies include connection establishment in TCP and a priority queue from the Java Class Library.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Characteristic classes of Q-manifolds: Classification and applications

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Mosman, E. A.; Sharapov, A. A.

2010-05-01

A Q-manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative LQ along Q makes the algebra of smooth tensor fields on M into a differential algebra. In this paper, we define and study the invariants of Q-manifolds called characteristic classes. These take values in the cohomology of the operator LQ and, given an affine symmetric connection with curvature R, can be represented by universal tensor polynomials in the repeated covariant derivatives of Q and R up to some finite order. As usual, the characteristic classes are proved to be independent of the choice of the affine connection used to define them. The main result of the paper is a complete classification of the intrinsic characteristic classes, which, by definition, do not vanish identically on flat Q-manifolds. As an illustration of the general theory we interpret some of the intrinsic characteristic classes as anomalies in the BV and BFV-BRST quantization methods of gauge theories. An application to the theory of (singular) foliations is also discussed.

On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback

NASA Astrophysics Data System (ADS)

Razgulin, A. V.; Sazonova, S. V.

2017-09-01

A novel statement of the Fourier filtering problem based on the use of matrix Fourier filters instead of conventional multiplier filters is considered. The basic properties of the matrix Fourier filtering for the filters in the Hilbert-Schmidt class are established. It is proved that the solutions with a finite energy to the periodic initial boundary value problem for the quasi-linear functional differential diffusion equation with the matrix Fourier filtering Lipschitz continuously depend on the filter. The problem of optimal matrix Fourier filtering is formulated, and its solvability for various classes of matrix Fourier filters is proved. It is proved that the objective functional is differentiable with respect to the matrix Fourier filter, and the convergence of a version of the gradient projection method is also proved.

A Construction of Rigid Analytic Cohomology Classes for Split Reductive Algebraic Groups

NASA Astrophysics Data System (ADS)

Graham, Bonita Lynn

The cohomology groups H1(Gamma 0(N), Vk) completely describe the space of classical cusp forms of weight k and level N. We study a generalization, Hn(Gamma, Vlambda), where some algebraic group G plays a role analogous to that of GL2 in the classical case. Ash and Stevens proved that certain classes in Hn(Gamma, Vlambda) may be lifted through the natural map rho lambda : Hn(Gamma, D lambda) → Hn(Gamma, Vlambda) to overconvergent classes in H n(Gamma, Dlambda). Pollack and Pollack were able to prove this result constructively in the case of G = GL3, by providing a filtration on the distribution space D?. We construct a general filtration FilN D lambda, for a split reductive algebraic group G. Using this filtration, we are able to lift classes in Hn(Gamma, Vlambda) to the finite dimensional spaces H n(Gamma, Dlambda / FilN Dlambda). These lifts approximate the lifts into Hn(Gamma, Dlambda ) and improve as N → infinity.

Computational techniques for flows with finite-rate condensation

NASA Technical Reports Server (NTRS)

Candler, Graham V.

1993-01-01

A computational method to simulate the inviscid two-dimensional flow of a two-phase fluid was developed. This computational technique treats the gas phase and each of a prescribed number of particle sizes as separate fluids which are allowed to interact with one another. Thus, each particle-size class is allowed to move through the fluid at its own velocity at each point in the flow field. Mass, momentum, and energy are exchanged between each particle class and the gas phase. It is assumed that the particles do not collide with one another, so that there is no inter-particle exchange of momentum and energy. However, the particles are allowed to grow, and therefore, they may change from one size class to another. Appropriate rates of mass, momentum, and energy exchange between the gas and particle phases and between the different particle classes were developed. A numerical method was developed for use with this equation set. Several test cases were computed and show qualitative agreement with previous calculations.

Classifier performance prediction for computer-aided diagnosis using a limited dataset.

PubMed

Sahiner, Berkman; Chan, Heang-Ping; Hadjiiski, Lubomir

2008-04-01

In a practical classifier design problem, the true population is generally unknown and the available sample is finite-sized. A common approach is to use a resampling technique to estimate the performance of the classifier that will be trained with the available sample. We conducted a Monte Carlo simulation study to compare the ability of the different resampling techniques in training the classifier and predicting its performance under the constraint of a finite-sized sample. The true population for the two classes was assumed to be multivariate normal distributions with known covariance matrices. Finite sets of sample vectors were drawn from the population. The true performance of the classifier is defined as the area under the receiver operating characteristic curve (AUC) when the classifier designed with the specific sample is applied to the true population. We investigated methods based on the Fukunaga-Hayes and the leave-one-out techniques, as well as three different types of bootstrap methods, namely, the ordinary, 0.632, and 0.632+ bootstrap. The Fisher's linear discriminant analysis was used as the classifier. The dimensionality of the feature space was varied from 3 to 15. The sample size n2 from the positive class was varied between 25 and 60, while the number of cases from the negative class was either equal to n2 or 3n2. Each experiment was performed with an independent dataset randomly drawn from the true population. Using a total of 1000 experiments for each simulation condition, we compared the bias, the variance, and the root-mean-squared error (RMSE) of the AUC estimated using the different resampling techniques relative to the true AUC (obtained from training on a finite dataset and testing on the population). Our results indicated that, under the study conditions, there can be a large difference in the RMSE obtained using different resampling methods, especially when the feature space dimensionality is relatively large and the sample size is small. Under this type of conditions, the 0.632 and 0.632+ bootstrap methods have the lowest RMSE, indicating that the difference between the estimated and the true performances obtained using the 0.632 and 0.632+ bootstrap will be statistically smaller than those obtained using the other three resampling methods. Of the three bootstrap methods, the 0.632+ bootstrap provides the lowest bias. Although this investigation is performed under some specific conditions, it reveals important trends for the problem of classifier performance prediction under the constraint of a limited dataset.

Finite-size analysis of the detectability limit of the stochastic block model

NASA Astrophysics Data System (ADS)

Young, Jean-Gabriel; Desrosiers, Patrick; Hébert-Dufresne, Laurent; Laurence, Edward; Dubé, Louis J.

2017-06-01

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.

Anderson metal-insulator transitions with classical magnetic impurities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Daniel; Kettemann, Stefan

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition (AMIT) numerically. In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude W{sub c}, in the presence of Heisenberg impurities, W{sub c} is first increased with increasing exchange coupling strength J due to time-reversal symmetry breaking. The resulting scaling with J is compared to analytical predictions by Wegner [1]. The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [2], which is the geometric average of the local densitymore » of states. The latter can efficiently be calculated using the kernel polynomial method [3]. Although still suffering from methodical shortcomings, our method proves to deliver results close to established results for the orthogonal symmetry class [4]. We extend previous approaches [5] by combining the KPM with a finite-size scaling analysis. We also discuss the relevance of our findings for systems like phosphor-doped silicon (Si:P), which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [6].« less

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

An entropy maximization problem related to optical communication

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Rodemich, E. R.; Swanson, L.

1986-01-01

In relation to a problem in optical communication, the paper considers the general problem of maximizing the entropy of a stationary radom process that is subject to an average transition cost constraint. By using a recent result of Justesen and Hoholdt, an exact solution to the problem is presented and a class of finite state encoders that give a good approximation to the exact solution is suggested.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gravitational waves

NASA Astrophysics Data System (ADS)

Rabinovich, B. I.

2006-01-01

The model problem of the dynamics of a planar plasma ring rotating in the dipole magnetic field of a central body is considered. A finite-dimensional mathematical model of the system is synthesized by the Boubnov-Galerkin method. The class of solutions corresponding to magneto-gravitational waves associated with deformations of the ring boundaries is investigated.

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barker, Andrew T.; Benson, Thomas R.; Lee, Chak Shing

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

Three-dimensional analysis of cavity wall deformation after composite restoration of masticatory teeth.

PubMed

Manchorova-Veleva, Neshka A

2011-01-01

The aim of the present work was to study the size of cavity wall deformation in eight class I and II defects after composite restoration. 1. Creating a geometric model - data on the size of the left maxillary second premolar were obtained from a routine craniofacial scanning of a 20-year-old patient with a 2,5 Dental CT scanner (General Electric), with high resolution and 0.625mm-thin slices. The contour of each of the 33 cross-sections of tooth 25 was delineated using graphics software (CorelDraw 7.0) and transferred to a specialized product for engineering design (SolidWorks Office Premium 2010, SolidWorks Corp. USA). The pulp cavity and periodontal ligament were created in the same manner and were integrated in the premolar body; 2. Generation of a finite element method - the geometric model was exported to specialized software for analysis by the finite element method - COSMOSWorks 2010, which automatically builds a 3D finite elements mesh. Based on the generated model, eight additional models of class I and II cavities with different geometries, adhesive layer and nanofilled composite restorations were constructed. The polymerization shrinkage was modelled by thermal deformation, with a negative temperature difference (cooling), corresponding to the actual volume shrinkage of the composite materials by 2.1%. In models A and B, the maximum cavity wall displacement was small - 0.014 mm and 0.015 mm, respectively. In models Al, B1, C1 and C, the displacement was at the expense of large deformation of the dental tissues. The maximum cavity wall displacements were 0.020 mm, 0.026 mm, 0.020 mm, 0.035 mm, respectively. The least cavity wall displacement was in models A2 and B2 with 0.008 mm and 0.017 mm, respectively. The least displacement resulting from cavity wall deformation is found in patient-friendly class I and II preparations. Preservation of the dental tissues reduces the risk of mechanical pressure on the dentinal lymph and the likelihood of post-operative sensitivity.

Development of an object-oriented finite element program: application to metal-forming and impact simulations

NASA Astrophysics Data System (ADS)

Pantale, O.; Caperaa, S.; Rakotomalala, R.

2004-07-01

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations.

The discrete prolate spheroidal filter as a digital signal processing tool

NASA Technical Reports Server (NTRS)

Mathews, J. D.; Breakall, J. K.; Karawas, G. K.

1983-01-01

The discrete prolate spheriodall (DPS) filter is one of the glass of nonrecursive finite impulse response (FIR) filters. The DPS filter is superior to other filters in this class in that it has maximum energy concentration in the frequency passband and minimum ringing in the time domain. A mathematical development of the DPS filter properties is given, along with information required to construct the filter. The properties of this filter were compared with those of the more commonly used filters of the same class. Use of the DPS filter allows for particularly meaningful statements of data time/frequency resolution cell values. The filter forms an especially useful tool for digital signal processing.

Universality classes of foraging with resource renewal

NASA Astrophysics Data System (ADS)

Chupeau, M.; Bénichou, O.; Redner, S.

2016-03-01

We determine the impact of resource renewal on the lifetime of a forager that depletes its environment and starves if it wanders too long without eating. In the framework of a minimal starving random-walk model with resource renewal, there are three universal classes of behavior as a function of the renewal time. For sufficiently rapid renewal, foragers are immortal, while foragers have a finite lifetime otherwise. In the specific case of one dimension, there is a third regime, for sufficiently slow renewal, in which the lifetime of the forager is independent of the renewal time. We outline an enumeration method to determine the mean lifetime of the forager in the mortal regime.

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Vinokur, M.

1979-01-01

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent.

Finite element model of size, shape and blood pressure on rupture of intracranial saccular aneurysms

NASA Astrophysics Data System (ADS)

Rica Nabong, Jennica; David, Guido

2017-10-01

Rupture of intracranial saccular aneurysms is a primary concern for neurologists and patients because it leads to stroke and permanent disability. This paper examines the role of blood pressure, in connection with size of and wall thickness, in the rupture of saccular aneurysms. A bulb-shaped geometry of a saccular aneurysm is obtained from angiographic images of a patient and modeled using Finite Elements based on the principle of virtual work under the Fung stress-strain relationship. The numerical model is subjected to varying levels of systolic blood pressure. Rupture is assumed to occur when the wall stress exceeded its mechanical strength. The results show which sizes of this class of aneurysms are at high risk of rupture for varying levels of blood pressure.

A description of discrete internal representation schemes for visual pattern discrimination.

PubMed

Foster, D H

1980-01-01

A general description of a class of schemes for pattern vision is outlined in which the visual system is assumed to form a discrete internal representation of the stimulus. These representations are discrete in that they are considered to comprise finite combinations of "components" which are selected from a fixed and finite repertoire, and which designate certain simple pattern properties or features. In the proposed description it is supposed that the construction of an internal representation is a probabilistic process. A relationship is then formulated associating the probability density functions governing this construction and performance in visually discriminating patterns when differences in pattern shape are small. Some questions related to the application of this relationship to the experimental investigation of discrete internal representations are briefly discussed.

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

Finite-time scaling at the Anderson transition for vibrations in solids

NASA Astrophysics Data System (ADS)

Beltukov, Y. M.; Skipetrov, S. E.

2017-11-01

A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame exhibits an Anderson localization transition. To study this transition, we assume that the dynamical matrix of the network is given by a product of a sparse random matrix with real, independent, Gaussian-distributed nonzero entries and its transpose. A finite-time scaling analysis of the system's response to an initial excitation allows us to estimate the critical parameters of the localization transition. The critical exponent is found to be ν =1.57 ±0.02 , in agreement with previous studies of the Anderson transition belonging to the three-dimensional orthogonal universality class.

Tsallis thermostatistics for finite systems: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.

2003-05-01

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.

Scalable algorithms for three-field mixed finite element coupled poromechanics

NASA Astrophysics Data System (ADS)

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

2016-12-01

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

Sudden death of entanglement and non-locality in two- and three-component quantum systems

NASA Astrophysics Data System (ADS)

Ann, Kevin

2011-12-01

Quantum entanglement and non-locality are non-classical characteristics of quantum states with phase coherence that are of central importance to physics, and relevant to the foundations of quantum mechanics and quantum information science. This thesis examines quantum entanglement and non-locality in two- and three-component quantum states with phase coherence when they are subject to statistically independent, classical, Markovian, phase noise in various combinations at the local and collective level. Because this noise reduces phase coherence, it can also reduce quantum entanglement and Bell non-locality. After introducing and contextualizing the research, the results are presented in three broad areas. The first area characterizes the relative time scales of decoherence and disentanglement in 2 x 2 and 3 x 3 quantum states, as well as the various subsystems of the two classes of entangled tripartite two-level quantum states. In all cases, it was found that disentanglement time scales are less than or equal to decoherence time scales. The second area examines the finite-time loss of entanglement, even as quantum state coherence is lost only asymptotically in time due to local dephasing noise, a phenomenon entitled "Entanglement Sudden Death" (ESD). Extending the initial discovery in the simplest 2 x 2 case, ESD is shown to exist in all other systems where mixed-state entanglement measures exist, the 2 x 3 and d x d systems, for finite d > 2. The third area concerns non-locality, which is a physical phenomenon independent of quantum mechanics and related to, though fundamentally different from, entanglement. Non-locality, as quantified by classes of Bell inequalities, is shown to be lost in finite time, even when decoherence occurs only asymptotically. This phenomenon was named "Bell Non-locality Sudden Death" (BNSD).

Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds

NASA Astrophysics Data System (ADS)

Blumen, Sacha C.

2006-01-01

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra U_q(osp(1|2n)) over C is considered with q a primitive N^th root of unity for all integers N >= 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U_q^(N)(osp(1|2n)) = U_q(osp(1|2n)) / I is a Z_2-graded ribbon Hopf algebra. For all n and all N >= 3, a finite collection of finite dimensional representations of U_q^(N)(osp(1|2n)) is defined. Each such representation of U_q^(N)(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U_q^(N)(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N >= 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.

Surface sampling techniques for 3D object inspection

NASA Astrophysics Data System (ADS)

Shih, Chihhsiong S.; Gerhardt, Lester A.

1995-03-01

While the uniform sampling method is quite popular for pointwise measurement of manufactured parts, this paper proposes three novel sampling strategies which emphasize 3D non-uniform inspection capability. They are: (a) the adaptive sampling, (b) the local adjustment sampling, and (c) the finite element centroid sampling techniques. The adaptive sampling strategy is based on a recursive surface subdivision process. Two different approaches are described for this adaptive sampling strategy. One uses triangle patches while the other uses rectangle patches. Several real world objects were tested using these two algorithms. Preliminary results show that sample points are distributed more closely around edges, corners, and vertices as desired for many classes of objects. Adaptive sampling using triangle patches is shown to generally perform better than both uniform and adaptive sampling using rectangle patches. The local adjustment sampling strategy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. In a hybrid approach, uniform points sets and non-uniform points sets, first preprocessed by the adaptive sampling algorithm on a real world object were then tested using the local adjustment sampling method. The results show that the initial point sets when preprocessed by adaptive sampling using triangle patches, are moved the least amount of distance by the subsequently applied local adjustment method, again showing the superiority of this method. The finite element sampling technique samples the centroids of the surface triangle meshes produced from the finite element method. The performance of this algorithm was compared to that of the adaptive sampling using triangular patches. The adaptive sampling with triangular patches was once again shown to be better on different classes of objects.

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

NASA Technical Reports Server (NTRS)

Hall, Philip; Balakumar, P.

1990-01-01

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Classification of cryo electron microscopy images, noisy tomographic images recorded with unknown projection directions, by simultaneously estimating reconstructions and application to an assembly mutant of Cowpea Chlorotic Mottle Virus and portals of the bacteriophage P22

NASA Astrophysics Data System (ADS)

Lee, Junghoon; Zheng, Yili; Yin, Zhye; Doerschuk, Peter C.; Johnson, John E.

2010-08-01

Cryo electron microscopy is frequently used on biological specimens that show a mixture of different types of object. Because the electron beam rapidly destroys the specimen, the beam current is minimized which leads to noisy images (SNR substantially less than 1) and only one projection image per object (with an unknown projection direction) is collected. For situations where the objects can reasonably be described as coming from a finite set of classes, an approach based on joint maximum likelihood estimation of the reconstruction of each class and then use of the reconstructions to label the class of each image is described and demonstrated on two challenging problems: an assembly mutant of Cowpea Chlorotic Mottle Virus and portals of the bacteriophage P22.

Estimation and Analysis of Nonlinear Stochastic Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Marcus, S. I.

1975-01-01

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

A class of semiparametric cure models with current status data.

PubMed

Diao, Guoqing; Yuan, Ao

2018-02-08

Current status data occur in many biomedical studies where we only know whether the event of interest occurs before or after a particular time point. In practice, some subjects may never experience the event of interest, i.e., a certain fraction of the population is cured or is not susceptible to the event of interest. We consider a class of semiparametric transformation cure models for current status data with a survival fraction. This class includes both the proportional hazards and the proportional odds cure models as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the maximum likelihood estimators for the regression coefficients are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in finite samples. For illustration, we provide an application of the models to a study on the calcification of the hydrogel intraocular lenses.

Manipulatable Andreev reflection due to the interplay between the DIII-class topological and s-wave superconductors

NASA Astrophysics Data System (ADS)

Wang, Xiao-Qi; Yi, Guang-Yu; Han, Yu; Jiang, Cui; Gong, Wei-Jiang

2018-07-01

We construct one mesoscopic circuit in which one quantum dot couples to one DIII-class topological superconductor and one s-wave superconductor, in addition to its connection with the metallic lead. And then, the Andreev reflection current in the metallic lead is evaluated. It is found that the two kinds of superconductors drive the Andreev reflection in the constructive manner. Next as finite superconducting phase difference is taken into account, the Andreev reflection oscillates in period π/2, and it can be suppressed in the low-energy region if the superconducting phase difference is (n + 1/2) π/2 (n ∈ Integer). Such a result is almost independent of the increase of the intradot Coulomb interaction. Therefore, this structure can assist to realize the manipulation of the Andreev reflection. Also, the result in this work provides useful information for understanding the property of the DIII-class topological superconductor.

Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field.

PubMed

Dias, D A; Xavier, J C; Plascak, J A

2017-01-01

The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons.

PubMed

Ratas, Irmantas; Pyragas, Kestutis

2016-09-01

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.

High-order asynchrony-tolerant finite difference schemes for partial differential equations

NASA Astrophysics Data System (ADS)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

Test-Analysis Correlation of a Crash Simulation of a Vertical Drop Test of a Commuter-Category Aircraft

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.

2004-01-01

A finite element model of an ATR42-300 commuter-class aircraft was developed and a crash simulation was executed. Analytical predictions were correlated with data obtained from a 30-feet per second (9.14-meters per second) vertical drop test of the aircraft. The purpose of the test was to evaluate the structural response of the aircraft when subjected to a severe, but survivable, impact. The aircraft was configured with seats, dummies, luggage, and other ballast. The wings were filled with 8,700 lb. (3,946 kilograms) of water to represent the fuel. The finite element model, which consisted of 57,643 nodes and 62,979 elements, was developed from direct measurements of the airframe geometry. The seats, dummies, luggage, simulated engines and fuel, and other ballast were represented using concentrated masses. The model was executed in LS-DYNA, a commercial finite element code for performing explicit transient dynamic simulations. Analytical predictions of structural deformation and selected time-history responses were correlated with experimental data from the drop test to validate the simulation.

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-06-01

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized three-dimensional (3D) compressible Navier-Stokes equations. A complete semi-discrete entropy estimate for the interior domain is achieved combining a discontinuous entropy conservative operator of any order [1,2] with an entropy stable coupling condition for the inviscid terms, and a local discontinuous Galerkin (LDG) approach with an interior penalty (IP) procedure for the viscous terms. The viscous penalty contributions scale with the inverse of the Reynolds number (Re) so that for Re → ∞ their contributions vanish and only the entropy stable inviscid interface penalty term is recovered. This paper extends the interface couplings presented [1,2] and provides a simple and automatic way to compute the magnitude of the viscous IP term. The approach presented herein is compatible with any diagonal norm summation-by-parts (SBP) spatial operator, including finite element, finite volume, finite difference schemes and the class of high-order accurate methods which include the large family of discontinuous Galerkin discretizations and flux reconstruction schemes.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Deformations of super Riemann surfaces

NASA Astrophysics Data System (ADS)

Ninnemann, Holger

1992-11-01

Two different approaches to (Kostant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincaré upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function.

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

NASA Astrophysics Data System (ADS)

Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor

2016-10-01

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the R-matrix structure and the structure of DIM algebra intertwiners, i.e. of refined topological vertices and show that the R-matrix is diagonalized by the action of the spectral duality belonging to the SL(2, ℤ) group of DIM algebra automorphisms. We also construct the T-operators satisfying the RTT relations with the R-matrix from refined amplitudes on resolved conifold. We thus show that topological string theories on the toric Calabi-Yau threefolds can be naturally interpreted as lattice integrable models. Integrals of motion for these systems are related to q-deformation of the reflection matrices of the Liouville/Toda theories.

A well-behaved class of charged analogue of Durgapal solution

NASA Astrophysics Data System (ADS)

Mehta, R. N.; Pant, Neeraj; Mahto, Dipo; Jha, J. S.

2013-02-01

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. This solution gives us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. Keeping in view of well behaved nature of this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤ K≤2.2) for which the solution is well behaved hence, suitable for modeling of super dense stars like strange quark stars, neutron stars and pulsars. For this class of solution the mass of a star is maximized with all degree of suitability, compatible with quark stars, neutron stars and pulsars. By assuming the surface density ρ b =2×1014 g/cm3 (like, Brecher and Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03 M Θ , radius r b =19.53 km and moment of inertia I=1.213×1046 g cm2; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43 M Θ , radius r b =18.04 km and moment of inertia I=1.136×1046 g cm2; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56 M Θ , radius r b =17.30 km and moment of inertia I=1.076×1046 g cm2. These values of masses and moment of inertia are found to be consistent with the crab pulsars.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2010-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Evidence of singularities for a family of contour dynamics equations

PubMed Central

Córdoba, Diego; Fontelos, Marco A.; Mancho, Ana M.; Rodrigo, Jose L.

2005-01-01

In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < α ≤ 1. The limiting case α → 0 corresponds to 2D Euler equations, and α = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner. PMID:15837929

Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

NASA Astrophysics Data System (ADS)

Brannan, Michael; Collins, Benoît

2018-03-01

In this paper we describe a class of highly entangled subspaces of a tensor product of finite-dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of d-positive maps on matrix algebras is also presented.

A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands

Treesearch

Lianjun Zhang; Jeffrey H. Gove; Chuangmin Liu; William B. Leak

2001-01-01

The rotated-sigmoid form is a characteristic of old-growth, uneven-aged forest stands caused by past disturbances such as cutting, fire, disease, and insect attacks. The diameter frequency distribution of the rotated-sigmoid form is bimodal with the second rounded peak in the midsized classes, rather than a smooth, steeply descending, monotonic curve. In this study a...

Performance Comparison of Superresolution Array Processing Algorithms. Revised

DTIC Science & Technology

1998-06-15

plane waves is finite is the MUSIC algorithm [16]. MUSIC , which denotes Multiple Signal Classification, is an extension of the method of Pisarenko [18... MUSIC Is but one member of a class of methods based upon the decomposition of covariance data into eigenvectors and eigenvalues. Such techniques...techniques relative to the classical methods, however, results for MUSIC are included in this report. All of the techniques reviewed have application to

On representations of the filiform Lie superalgebra Lm,n

NASA Astrophysics Data System (ADS)

Wang, Qi; Chen, Hongjia; Liu, Wende

2015-11-01

In this paper, we study the representations for the filiform Lie superalgebras Lm,n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over Lm,n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over Lm,n on the Grassmann algebra and the mixed Clifford-Weyl algebra.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J. N.; Turner, J. D.; Chun, H. M.

1986-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

On the spline-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Algorithm for Surface of Translation Attached Radiators (A-STAR). Volume 1: Formulation of the analysis

NASA Astrophysics Data System (ADS)

Medgyesimitschang, L. N.; Putnam, J. M.

1982-05-01

A general analytical formulation, based on the method of moments (MM) is described for solving electromagnetic problems associated with off-surface (wire) and aperture radiators on finite-length cylinders of arbitrary cross section, denoted in this report as bodies of translation (BOT). This class of bodies can be used to model structures with noncircular cross sections such as wings, fins and aircraft fuselages.

Switching Systems: Controllability and Control Design

DTIC Science & Technology

2009-04-25

controllable linear time invariant (LTI) systems ẋ = Ax+Bu are stabilizable and the stabilization can be always done by a...to control the system is bounded. As an application controllability conditions for a class of bimodal linear time invariant (LTI) systems are also...There exist a universal ( finite ) switching sequence σ such that the time varying system ẋ = A(σ)x+ B(σ)u is globally controllable . Proof: The

Interframe vector wavelet coding technique

NASA Astrophysics Data System (ADS)

Wus, John P.; Li, Weiping

1997-01-01

Wavelet coding is often used to divide an image into multi- resolution wavelet coefficients which are quantized and coded. By 'vectorizing' scalar wavelet coding and combining this with vector quantization (VQ), vector wavelet coding (VWC) can be implemented. Using a finite number of states, finite-state vector quantization (FSVQ) takes advantage of the similarity between frames by incorporating memory into the video coding system. Lattice VQ eliminates the potential mismatch that could occur using pre-trained VQ codebooks. It also eliminates the need for codebook storage in the VQ process, thereby creating a more robust coding system. Therefore, by using the VWC coding method in conjunction with the FSVQ system and lattice VQ, the formulation of a high quality very low bit rate coding systems is proposed. A coding system using a simple FSVQ system where the current state is determined by the previous channel symbol only is developed. To achieve a higher degree of compression, a tree-like FSVQ system is implemented. The groupings are done in this tree-like structure from the lower subbands to the higher subbands in order to exploit the nature of subband analysis in terms of the parent-child relationship. Class A and Class B video sequences from the MPEG-IV testing evaluations are used in the evaluation of this coding method.

Applied mathematical problems in modern electromagnetics

NASA Astrophysics Data System (ADS)

Kriegsman, Gregory

1994-05-01

We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.

Global stabilisation of a class of generalised cascaded systems by homogeneous method

NASA Astrophysics Data System (ADS)

Ding, Shihong; Zheng, Wei Xing

2016-04-01

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot.

Social interaction anxiety and personality traits predicting engagement in health risk sexual behaviors.

PubMed

Rahm-Knigge, Ryan L; Prince, Mark A; Conner, Bradley T

2018-06-01

Individuals with social interaction anxiety, a facet of social anxiety disorder, withdraw from or avoid social encounters and generally avoid risks. However, a subset engages in health risk sexual behavior (HRSB). Because sensation seeking, emotion dysregulation, and impulsivity predict engagement in HRSB among adolescents and young adults, the present study hypothesized that latent classes of social interaction anxiety and these personality traits would differentially predict likelihood of engagement in HRSB. Finite mixture modeling was used to discern four classes: two low social interaction anxiety classes distinguished by facets of emotion dysregulation, positive urgency, and negative urgency (Low SIAS High Urgency and Low SIAS Low Urgency) and two high social interaction anxiety classes distinguished by positive urgency, negative urgency, risk seeking, and facets of emotion dysregulation (High SIAS High Urgency and High SIAS Low Urgency). HRSB were entered into the model as auxiliary distal outcomes. Of importance to this study were findings that the High SIAS High Urgency class was more likely to engage in most identified HRSB than the High SIAS Low Urgency class. This study extends previous findings on the heterogeneity of social interaction anxiety by identifying the effects of social interaction anxiety and personality on engagement in HRSB. Copyright © 2018 Elsevier Ltd. All rights reserved.

A general model to explore complex dominance patterns in plant sporophytic self-incompatibility systems.

PubMed

Billiard, Sylvain; Castric, Vincent; Vekemans, Xavier

2007-03-01

We developed a general model of sporophytic self-incompatibility under negative frequency-dependent selection allowing complex patterns of dominance among alleles. We used this model deterministically to investigate the effects on equilibrium allelic frequencies of the number of dominance classes, the number of alleles per dominance class, the asymmetry in dominance expression between pollen and pistil, and whether selection acts on male fitness only or both on male and on female fitnesses. We show that the so-called "recessive effect" occurs under a wide variety of situations. We found emerging properties of finite population models with several alleles per dominance class such as that higher numbers of alleles are maintained in more dominant classes and that the number of dominance classes can evolve. We also investigated the occurrence of homozygous genotypes and found that substantial proportions of those can occur for the most recessive alleles. We used the model for two species with complex dominance patterns to test whether allelic frequencies in natural populations are in agreement with the distribution predicted by our model. We suggest that the model can be used to test explicitly for additional, allele-specific, selective forces.

Development of an hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1993-01-01

The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.

The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marcer, Peter J.; Rowlands, Peter

2010-11-24

The universal nilpotent computational rewrite system (UNCRS) is shown to formalize an irreversible process of evolution in conformity with the First, Second and Third Laws of Thermodynamics, in terms of a single algebraic creation operator (ikE+ip+jm) which delivers the whole quantum mechanical language apparatus, where k, i, j are quaternions units and E, p, m are energy, momentum and rest mass. This nilpotent evolution describes 'a dynamic zero totality universe' in terms of its fermion states (each of which, by Pauli exclusion, is unique and nonzero), where, together with their boson interactions, these define physics at the fundamental level. (Themore » UNCRS implies that the inseparability of objects and fields in the quantum universe is based on the fact that the only valid mathematical representations are all automorphisms of the universe itself, and that this is the mathematical meaning of quantum entanglement. It thus appears that the nilpotent fermion states are in fact what is called the splitting field in Quantum Mechanics of the Galois group which leads to the roots of the corresponding algebraic equation, and concerns in this case the alternating group of even permutations which are themselves automorphisms). In the nilpotent evolutionary process: (i) the Quantum Carnot Engine (QCE) extended model of thermodynamic irreversibility, consisting of a single heat bath of an ensemble of Standard Model elementary particles, retains a small amount of quantum coherence / entanglement, so as to constitute new emergent fermion states of matter, and (ii) the metric (E{sup 2}-p{sup 2}m{sup 2}) = 0 ensures the First Law of the conservation of energy operates at each nilpotent stage, so that (iii) prior to each creation (and implied corresponding annihilation / conserve operation), E and m can be postulated to constitute dark energy and matter respectively. It says that the natural language form of the rewrite grammar of the evolution consists of the well known precepts of the Laws of Thermodynamics, formalized by the UNCRS regress, so as to become (as UNCRS rewrites already published at CASYS), firstly the Quantum Laws of Physics in the form of the generalized Dirac equation and later at higher stages of QCE ensemble complexity, the Laws of Life in the form of Nature's (DNA / RNA genetic) Code and then subsequently those of Intelligence and Consciousness (Nature's Rules).« less

Magnetic helices as metastable states of finite XY ferromagnetic chains: An analytical study

NASA Astrophysics Data System (ADS)

Popov, Alexander P.; Pini, Maria Gloria

2018-04-01

We investigated a simple but non trivial model, consisting of a chain of N classical XY spins with nearest neighbor ferromagnetic interaction, where each of the two end-point spins is assumed to be exchange-coupled to a fully-pinned fictitious spin. In the mean field approximation, the system might be representative of a soft ferromagnetic film sandwiched between two magnetically hard layers. We show that, while the ground state is ferromagnetic and collinear, the system can attain non-collinear metastable states in the form of magnetic helices. The helical solutions and their stability were studied analytically in the absence of an external magnetic field. There are four possible classes of solutions. Only one class is metastable, and its helical states contain an integer number of turns. Among the remaining unstable classes, there is a class of helices which contain an integer number of turns. Therefore, an integer number of turns in a helical configuration is a necessary, but not a sufficient, condition for metastability. These results may be useful to devise future applications of metastable magnetic helices as energy-storing elements.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

A Robust Absorbing Boundary Condition for Compressible Flows

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; orgenson, Philip C. E.

2005-01-01

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elizalde, Emilio; Odintsov, Sergei D.; Pozdeeva, Ekaterina O.

2016-02-01

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflationmore » scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.« less

Computational modeling of electromechanical instabilities in dielectric elastomers (Conference Presentation)

NASA Astrophysics Data System (ADS)

Park, Harold

2016-04-01

Dielectric elastomers are a class of soft, active materials that have recently gained significant interest due to the fact that they can be electrostatically actuated into undergoing extremely large deformations. An ongoing challenge has been the development of robust and accurate computational models for elastomers, particularly those that can capture electromechanical instabilities that limit the performance of elastomers such as creasing, wrinkling, and snap-through. I discuss in this work a recently developed finite element model for elastomers that is dynamic, nonlinear, and fully electromechanically coupled. The model also significantly alleviates volumetric locking due that arises due to the incompressible nature of the elastomers, and incorporates viscoelasticity within a finite deformation framework. Numerical examples are shown that demonstrate the performance of the proposed method in capturing electromechanical instabilities (snap-through, creasing, cratering, wrinkling) that have been observed experimentally.

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Vinokur, M.

1983-01-01

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

BRST symmetry for a torus knot

NASA Astrophysics Data System (ADS)

Pandey, Vipul Kumar; Prasad Mandal, Bhabani

2017-08-01

We develop BRST symmetry for the first time for a particle on the surface of a torus knot by analyzing the constraints of the system. The theory contains 2nd-class constraints and has been extended by introducing the Wess-Zumino term to convert it into a theory with first-class constraints. BFV analysis of the extended theory is performed to construct BRST/anti-BRST symmetries for the particle on a torus knot. The nilpotent BRST/anti-BRST charges which generate such symmetries are constructed explicitly. The states annihilated by these nilpotent charges consist of the physical Hilbert space. We indicate how various effective theories on the surface of the torus knot are related through the generalized version of the BRST transformation with finite-field-dependent parameters.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Resolvent-Techniques for Multiple Exercise Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christensen, Sören, E-mail: christensen@math.uni-kiel.de; Lempa, Jukka, E-mail: jukka.lempa@hioa.no

2015-02-15

We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristicsmore » of the problems can be identified more explicitly. We illustrate the main results with explicit examples.« less

Cohomology of line bundles: Applications

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Jurke, Benjamin; Rahn, Thorsten; Roschy, Helmut

2012-01-01

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute cohomology for line bundles on finite group action coset spaces, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev's formula and its generalizations can be given a one-to-one cohomological interpretation. Furthermore, we derive a combinatorial closed form expression for two Hodge numbers of a codimension two Calabi-Yau fourfold.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Water: US Strategic Response to Conflicts Over a Finite Resource

DTIC Science & Technology

2009-02-25

World War II ended and the African nations became independent, this Victorian Era arrangement soon encountered serious problems. Sudan and 6 Ethiopia...Carlisle Barracks, PA 17013-5050 USAWC CLASS OF 2009 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection...conditions in an already hostile region. Additionally, India has already drawn down many of its aquifers in northern India; the 17 economic and social

Active Learning Using Arbitrary Binary Valued Queries

DTIC Science & Technology

1990-10-01

active learning in the sense that the learner has complete choice in the information received. Specifically, we allow the learner to ask arbitrary yes...no questions. We consider both active learning under a fixed distribution and distribution-free active learning . In the case of active learning , the...a concept class is actively learnable iff it is finite, so that active learning is in fact less powerful than the usual passive learning model. We

Special Issue: Tenth International Conference on Finite Elements in Fluids, Tucson, Arizona.Copyright © 1999 John Wiley & Sons, Ltd.Save Title to My Profile

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