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1.
A. Jánosi 《Zeitschrift für Physik B Condensed Matter》1990,80(3):393-400
We study the effects of some of the most important and typical structural changes in two-phase systems on selected structural parameters obtained from small-angle x-ray scattering (SAXS) measurements. To limit the present study, it was assumed that the Phase, 1, embedded in the matrix
- is monodispersed and homogeneous,
- possesses one of the three most extreme shapes (spherical, fibrillar or lamellar) and
- changes its behaviour
- through type change (spinodal or nucleotic or coarsening), without changing the shape,
- through a change of the shape only, or
- through a) (type change) and b) (shape change) simultaneously.
- chord lengthl 1 (and/or radius of gyrationR),
- volume partw 1 of the Phase 1, and
- relative inner surfaceS v of the system.
- spinodal change, all three SAXRS parameters are increasing or decreasing simultaneously and proportional to a power of the intensity of the change,
- nucleotic change,l 1 (and/orR) is unchanged, the other two (w 1 andS v ) are increasing or decreasing simultaneously and directly proportional to the intensity,
- coarsening change,w 1 is unchanged and anincreasing ofl 1 is always accompanied by adecreasing ofS v and vice versa.
2.
Michael Henle 《Communications in Mathematical Physics》1970,19(4):273-275
Theorem. Let a topological groupG be represented (a→φ a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that
- G is locally compact and separable,
- R′ is properly infinite,
- for anyT∈R,x,y∈H the function
3.
Inequalities on eigenvalues of the Schrödinger operator are re-examined in the case of spherically symmetric potentials. In particular, we obtain:
- A connection between the moments of order (n ? 1)/2 of the eigenvalues of a one-dimensional problem and the total number of bound statesN n, inn space dimensions;
- optimal bounds on the total number of bound states below a given energy in one dimension;
- alower bound onN 2;
- a self-contained proof of the inequality for α ≧ 0,n ≧ 3, leading to the optimalC 04,C 3;
- solutions of non-linear variation equations which lead, forn ≧ 7, to counter examples to the conjecture thatC 0n is given either by the one-bound state case or by the classic limit; at the same time a conjecture on the nodal structure of the wave functions is disproved.
4.
Stewart D. Johnson 《Communications in Mathematical Physics》1989,122(2):293-320
Families of unimodal maps satisfying
- T λ: [?1,1]?[?1,1] withT(±1)=?1 and |T λ ′ (1)|>1.
- T λ(x) isC 2 inx 2 and λ, and symmetric inx.
- T 0(0)=0,T 1(0)=1 with \(\frac{d}{{d\lambda }}\) T λ(0)>0
5.
The positive sign of theη-nucleon scattering lengthb ηN was predicted in [1] assuming the resonance mechanism for theπ ?p → ηn reaction. We demonstrate that
- the assumption about thet-channel mechanism of the reaction leads tob ηN < 0 and
- the experimental data on theη production cross section are equally compatible with both resonance andt-channel mechanisms.
6.
Fractal percolation or Mandelbrot percolation is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of slices) of these random sets. Although random, the geometry of those sets is quite regular. Our results imply that, denoting by $E\subset\mathbb{R}^{2}$ a typical realization of the fractal percolation on the plane,
- If $\dim_{\rm H}E<1$ then for all lines ? the orthogonal projection E ? of E to ? has the same Hausdorff dimension as E,
- If $\dim_{\rm H}E>1$ then for any smooth real valued function f which is strictly increasing in both coordinates, the image f(E) contains an interval.
7.
E. Mourre 《Communications in Mathematical Physics》1981,78(3):391-408
We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:
- its point spectrum is finite;
- its singular continuous spectrum is empty;
- its resolvent satisfies a class of a priori estimates.
8.
P. Steiner V. Kinsinger I. Sander B. Siegwart S. Hüfner C. Politis 《Zeitschrift für Physik B Condensed Matter》1987,67(1):19-23
XPS and UPS photoemission experiments on the highT c superconductors (T c ≈90 K) with nominal composition YBa2Cu3O9-y (y≈2) show the following:
- The density of electronic states at the Fermi energy is very small, much smaller than in pure Cu.
- The Cu 2p spectra show only a Cu2+ contribution.
- The Ba core levels show a structure with two components of nearly equal magnitude, which leads to the suggestion that these compounds have large O2? vacancies coordinated to Ba2+ sites.
- Annealing at 400°C under UHV conditions leads possibly to a partial reduction of Cu2+ to lower Cu valence states and to a small increase of the O2? vacancy component of the Ba2+ line.
9.
K. R. Ito 《Communications in Mathematical Physics》1982,83(4):537-561
Let ν=detren(1+K g ) be the renormalized Matthews-Salam determinant of (QED)2, where \(K_g = ieA_{g,} S = \left( {\sum {\gamma _\mu \partial } _\mu + m} \right)^{ - 1} \) is euclidean fermion propagator of one of the following boundary conditions: (1) free, (2) periodic at ?Λ, Λ=[?L/2;L/2]2, (3) anti-periodic at ?Λ, and \(A_g (x) = (\sum \gamma _\mu A_\mu (x))g(x)\) . Hereg(x)=1 ifxεΛ0=[?r/2,r/2]2 с Λ and 0 otherwise. Then we show
- νεL p (dμ(A)), p>0. Further we prove a new determinant inequality which holds for the QED, QCD-type models containing fermions. This enables us to prove:
- Z(Λ0)=∫νdμ(A)≦exp[c|Λ0|]. Similar volume dependence is shown for the Schwinger functions.
10.
J. C. M. Henning J. H. den Boef 《Applied Physics A: Materials Science & Processing》1978,16(4):353-357
A novel method for measuring magnetostriction constants is presented. A strain, periodic in time, applied to the sample, causes a modulation of the ferromagnetic resonance line position. The height of the signal obtained after phase-sensitive detection is proportional to the strain modulation depth. The appropriate magnetostriction constant λ is obtained by comparing the height of the SMFMR signal with that of the FMR line, as recorded by means of magnetic field modulation. Features of the new technique are:
- high sensitivity: λmin? 10?9 forM=100 Oe and linewidth ΔH d=1 Oe;
- λ's belonging to distinct precession modes are separately determined;
- applicable to thin layers for which strain gauge techniques cannot be used;
- wide temperature range: 1.2 K<T<300 K;
- uniform stress.
11.
12.
Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:
- The regularizedS δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
- The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
- The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ1=δ2=δ3=0.
- $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$
13.
It is demonstrated that a closed symmetric derivation δ of aC?-algebra \(\mathfrak{A}\) generates a strongly continuous one-parameter group of automorphisms of aC?-algebra \(\mathfrak{A}\) if and only if, it satisfies one of the following three conditions
- (αδ+1)(D(δ))= \(\mathfrak{A}\) , α∈?\{0}.
- δ possesses a dense set of analytic elements.
- δ possesses a dense set of geometric elements.
- ∥(αδ+1)(A)∥≧∥A∥, α∈IR,A∈D(δ).
- If α∈IR andA∈D(δ) then (αδ+1)(A)≧0 impliesA≧0.
14.
Francesco Pegoraro 《Communications in Mathematical Physics》1975,42(1):41-63
We consider a theorem due to Michel [1] which relates the invariance properties in peculiar directions in a linear space on which we represent a Lie groupG to the extremal points of an arbitrary smoothG-invariant function. The group we are interested in isSO(4) and we apply the mathematical results to the following problems:
- mixed linear Stark Zeeman effect in a hydrogen atom,
- perturbation of a finite Robertson-Walker metric,
- gas evolutions preserving angular momentum and vorticity.
15.
We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish
- If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
- The outgoing and incoming quasi-free fields coincide, there is no scattering.
- There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.
16.
J. Halbritter 《Applied Physics A: Materials Science & Processing》1986,39(1):49-57
Broad-area electrodes show electron emission already at electric field strengthsF≈107 V/m. This enhanced field emission (EFE) occurs only for contaminated surfaces. EFE is accompanied by photon emission and gas desorption yielding finally discharges. EFE is caused by dust and contaminants initiating the following effects: an electron is stochastically emitted in a trigger zone the electron gains energyΔE?eΔxF * which excites electronic states which relax by the emission of electrons, photons, and atoms where the positive charges left behind enhanceF *=βF (β?1) initiating so an electron avalanche, i.e., a high conductivity channel. Because of charge migration and neutralization, this avalanche has a life time. This pulsating EFE is accompanied by light emission and gas desorption yielding finally a gas cloud and a discharge. The pulsating, self-sustained EFE has the same root as: the enhanced secondary emission found first by Malter the conductivity switching exhibited by thin (≈ 1 μm) layers of semiconductors or insulators the normal cathode fall and the firing-wave instability in neurodynamics. 相似文献
17.
Stefano Moretti 《Zeitschrift fur Physik C Particles and Fields》1997,73(4):653-667
The complete matrix element for e + e? → bb?W+ W? is computed at tree-level within the Minimal Supersymmetric Standard Model. Rates of interest to phenomenological analyses at the Next Linear Collider are given. In particular, we study:
- ? tt? production and decay tt? →(bW +)(b?W ?)
- ? ZH production followed by Z → bb? and H → W + W?
- ? AH production followed by A→ bb? and H → W + W?
- ? hW + W? production followed by h→ bb?.
18.
Theq states Potts model exhibits a first order phase transition at some inverse temperature β t between “ordered” and “disordered” phases forq large as proved in [1]. In space dimension 2 we use theduality transformation as aninternal symmetry of the partition function at β t to derive an estimate on the probability of a contour. This enables us to prove the preceding result and the following new results:
- The discontinuity of the mass gap at β t .
- The existence of astrictly positive surface tension between two ordered phases up to β t .
- The existence of a non-zero surface tension between an “ordered” and the “disordered” phase at β t .
19.
G. T. Jones R. W. L. Jones D. R. O. Morrison M. M. Mobayyen S. Wainstein M. Aderholz D. Hantke E. Hoffmann U. F. Katz J. Kern N. Schmitz W. Wittek P. Allport H. P. Borner G. Myatt D. Radojicic F. W. Bullock S. Burke 《Zeitschrift fur Physik C Particles and Fields》1990,46(1):25-34
Using data onvp and \(\bar vp\) charged current interactions from a bubble chamber experiment with BEBC at CERN, the average multiplicities of charged hadrons and pions are determined as functions ofW 2 andQ 2. The analysis is based on ~20000 events with incidentv and ~10000 events with incident \(\bar v\) . In addition to the known dependence of the average multiplicity onW 2 a weak dependence onQ 2 for fixed intervals ofW is observed. ForW>2 GeV andQ 2>0.1 GeV2 the average multiplicity of charged hadrons is well described by〈n〉=a 1+a 2ln(W 2/GeV2)+a 3ln(Q 2/GeV2) witha 1=0.465±0.053,a 2=1.211±0.021,a 3=0.103±0.014 for thevp anda 1=?0.372±0.073,a 2=1.245±0.028,a 3=0.093±0.015 for the \(\bar vp\) reaction. 相似文献
20.
In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the following steady problem: $$v \cdot \nabla _{x}F =\frac{1}{{\rm K}_{\rm n}}Q(F,F),\qquad (x,v)\in \Omega \times \mathbf{R}^{3}, \quad \quad (0.1) $$ v · ? x F = 1 K n Q ( F , F ) , ( x , v ) ∈ Ω × R 3 , ( 0.1 ) $$F(x,v)|_{n(x)\cdot v<0} = \mu _{\theta}\int_{n(x) \cdot v^{\prime}>0}F(x,v^{\prime})(n(x)\cdot v^{\prime})dv^{\prime},\quad x \in\partial \Omega,\quad \quad (0.2) $$ F ( x , v ) | n ( x ) · v < 0 = μ θ ∫ n ( x ) · v ′ > 0 F ( x , v ′ ) ( n ( x ) · v ′ ) d v ′ , x ∈ ? Ω , ( 0.2 ) where Ω is a bounded domain in ${\mathbf{R}^{d}, 1 \leq d \leq 3}$ R d , 1 ≤ d ≤ 3 , Kn is the Knudsen number and ${\mu _{\theta}=\frac{1}{2\pi \theta ^{2}(x)} {\rm exp} [-\frac{|v|^{2}}{2\theta (x)}]}$ μ θ = 1 2 π θ 2 ( x ) exp [ - | v | 2 2 θ ( x ) ] is a Maxwellian with non-constant(non-isothermal) wall temperature θ(x). Based on new constructive coercivity estimates for both steady and dynamic cases, for ${|\theta -\theta_{0}|\leq \delta \ll 1}$ | θ - θ 0 | ≤ δ ? 1 and any fixed value of Kn, we construct a unique non-negative solution F s to (0.1) and (0.2), continuous away from the grazing set and exponentially asymptotically stable. This solution is a genuine non-equilibrium stationary solution differing from a local equilibrium Maxwellian. As an application of our results we establish the expansion ${F_s=\mu_{\theta_0}+\delta F_{1}+O(\delta ^{2})}$ F s = μ θ 0 + δ F 1 + O ( δ 2 ) and we prove that, if the Fourier law holds, the temperature contribution associated to F 1 must be linear, in the slab geometry. 相似文献