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  • 1
    Publication Date: 2023-12-20
    Keywords: HD28-70 ; bic Book Industry Communication::K Economics, finance, business & management::KJ Business & management::KJM Management & management techniques::KJMV Management of specific areas
    Language: German
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 85 (1982), S. 329-350 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We investigate the spectrum of Schrödinger operatorsH ω of the type:H ω=−Δ+∑q i (ω)f(x−x i +ζ i (ω))(q i (ω) and ζ i (ω) independent identically distributed random variables,i∈ℤ d ). We establish a strong connection between the spectrum ofH ω and the spectra of deterministic periodic Schrödinger operators. From this we derive a condition for the existence of “forbidden zones” in the spectrum ofH ω. For random one- and three-dimensional Kronig-Penney potentials the spectrum is given explicitly.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 89 (1983), S. 27-40 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the integrated density of states (IDS) ρ∞(λ) of random Hamiltonian Hω=−Δ+Vω, Vω being a random field on ℝ d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|−1ρ(λ, HΛ(ω)), Λ ⊂ ℝ d , around the thermodynamic limit ρ∞(λ) is bounded from above by exp {−k|Λ|},k〉0. In this case ρ∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ∞(λ) as λ → 0+ in the case where Vω is non-negative. More precisely we prove the following bound: ρ∞(λ)≦exp(−kλ−d/2) as λ → 0+ k〉0. This last result is then discussed in some examples.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Integral equations and operator theory 12 (1989), S. 383-391 
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 159 (1994), S. 459-469 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In the present paper, we discuss spectral properties of a periodic Schrödinger operator which is perturbed by randomly distributed impurities; such operators occur as simple models for crystals (or semi-conductors) with impurities. While the spectrum itself is independent of the concentrationp of impurities, for 0〈p〈1, we focus our attention on the limiting behavior of the integrated density of states ρ p of the random Schrödinger operator, inside a spectral gap of the periodic operator, asp→0. Denoting byU 0 the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located at the origin, say), we show that the integrated density of states concentrates around the points ofU 0, in the sense that ρ p (U ε) is of orderp, for any fixed ε-neighborhoodU ε ofU 0, while ρ p (K)≦C·p 2, for any compact subsetK of the gap which does not intersectU ε.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 195 (1998), S. 495-507 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for Schrödinger Operators with a periodic potential plus a random potential of the form , where $f$ decays at infinity like for m〉4d resp. $m〉3d depending on the regularity of f. The random variables q i are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical physics, analysis and geometry 2 (1999), S. 25-51 
    ISSN: 1572-9656
    Keywords: solitons ; sine-Gordon equation ; Marchenko equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An asymptotic analysis of the Marchenko integral equation for the sine-Gordon equation is presented. The results are used for a construction of soliton asymptotics of decreasing and some non-decreasing solutions of the sine-Gordon equation. The soliton phases are shown to have an additional shift with respect to the reflectionless case caused by the non-zero reflection coefficient of the corresponding Dirac operator. Explicit formulas for the phases are also obtained. The results demonstrate an interesting phenomenon of splitting of non-decreasing solutions into an infinite series of asymptotic solitons.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 80 (1995), S. 1-22 
    ISSN: 1572-9613
    Keywords: Random Schrödinger operators ; magnetic fields ; Lifshits tails
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the integrated density of states of the Schrödinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a nonnegative, algebraically decaying, single-impurity potential we prove that the leading asymptotic behavior for small energies is always given by the corresponding classical result, in contrast to the case of vanishing magnetic field. We also show that the integrated density of states of the operator restricted to the eingenspace of any Landau level exhibits the same behavior. For the lowest Landau level, this is in sharp contrast to the case of a Poisson random potential with a delta-function impurity potential.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Zeitschrift 232 (1999), S. 691-705 
    ISSN: 0025-5874
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We consider the Burgers equation with a periodic force $\frac{\partial}{\partial t}u+u\cdot\nabla u=\frac12\Delta u+\nabla V(x)$ which presents a simplified model for turbulence. We are interested in the asymptotic behaviour of solutions for $t\to\infty$ . This problem has been studied by Sinai who uses a probabilistic and very technical approach. Using methods from spectral theory we get similar results. This functional analytic approach gives an easier proof. For certain initial data (periodic or some random perturbations of those) we show time-convergence towards a deterministic periodic limit solution related to the ground state of a certain Schrödinger operator.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Weinheim [u.a.] : Wiley-Blackwell
    Materials and Corrosion/Werkstoffe und Korrosion 5 (1954), S. 452-454 
    ISSN: 0947-5117
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Corrosion protection of underground pipe lines by protective wrappingsDue to the many and varied properties of soils, anti-corrosion measures for protecting buried pipe lines present special problems. Usually such anti-corrosion measures consist of coatings of plastified bituminous compounds of varying thickness, which serve to insulate the pipe line from its surrounding soil.Steel pipes are usually delivered by the mill ready coated with some bituminous compound. The necessary protection of service pipes and joints is provided on the site by the use of prefabricated wrapping material. This consists of a foundation woven from some organic or inorganic fibres impregnated and coated with some protective material. Of late, plastic materials have been used with success. Such protection is applied by wrapping the material round the pipe so that each layer overlaps the preceding layer. If some heavy bituminous material is used, it is applied hot, so that a watertight covering shall result.Anti-corrosion methods consisting of a combination of well wrapped and insulated pipes and previous cathodic protection of the pipes promises to give particularly good results.
    Notes: An den Korrosionsschutz erdverlegter Rohrleitungen werden wegen der aggressiven Eigenschaften vieler Erdböden besondere Anforderungen gestellt. Meist besteht ein derartiger Korrosionsschutz aus einer mehr oder weniger dicken Umhüllung, von der man verlangt, daß sie das Rohr gegen seine Umgebung gut abdichtet.Stahlrohre erhalten in der Regel im Herstellungswerk bereits eine bituminöse Umhüllung. Fü das Nachisolieren auf der Baustelle sowie den Schutz von Hausanschlüssen und Rohrverbindungen benutzt man fertige Bandagen, die aus einem gewehten Träger aus organischen oder anorganischen Fasern mit einer Impräginerung und Auflagerung von Schutzmassen bestehen. Neuerdings werden mit gutem Erfolg auch Kunststoffe herangezogen. Die Aufbringung derartiger Schutzumhüllungen erfolgt im überlappenden Wickelverfahren, wobei im Falle der Verwendung dicker bituminöser Schutzbinden die Aufbringung unter Erwärmung erfolgt, um eine dichte Hülle zu gewinne.Eine Kombination des Korrosionsschutzes durch isolierende, gut abdichtende Bandagierung von Rohrleitungen mit dem kathodischen Schutzverfahren verspricht besonders gute Erfolge.
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