Infinite Volume Limit for the Stationary Distribution of Abelian Sandpile Models

We study the stationary distribution of the standard Abelian sandpile model in the box Λ_n = [-n, n] ^d ∩ ℤ ^d for d≥ 2. We show that as n→ ∞, the finite volume stationary distributions weakly converge to a translation invariant measure on allowed sandpile configurations in ℤ ^d . This allows us to define infinite volume versions of the avalanche-size distribution and related quantities. The proof is based on a mapping of the sandpile model to the uniform spanning tree due to Majumdar and Dhar, and the existence of the wired uniform spanning forest measure on ℤ ^d . In the case d > 4, we also make use of Wilson’s method. An erratum to this article is available at .     

<Emphasis Type="Italic">Λ</Emphasis>N scattering length from the reaction <Emphasis Type="Italic">γ</Emphasis>d→K<Superscript>+</Superscript><Emphasis Type="Italic">Λ</Emphasis>n

The prospects of utilizing the strangeness production reaction γd→K ⁺ Λn for the determination of the Λn low-energy scattering parameters are investigated. The spin observables that need to be measured in order to isolate the Λn singlet (¹ S ₀) and triplet (³ S ₁) states are identified. Possible kinematical regions where the extraction of the Λn scattering lengths might be feasible are discussed.     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

Entropic Repulsion for the High Dimensional Gaussian Lattice Field Between Two Walls

The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝ^λ _N , λ _N = [−N, N] ^d ∩ ℤ ^d and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ _N where L is large enough but finite. We also study the same problem for two layered interfaces case.     

Assessment of the possibility of determination of the electrophysical characteristics of CdxHg1–xTe p+–n-structures using differential hall measurements

The process of reconstuction of the distribution profile of hole concentration in the p ⁺–n structure by the method of differential Hall measurements upon implantation of ions As⁺ (Е = 190 keV, D = 3.10¹⁴ cm^-2, j = 0.025 μA/cm²) into epitaxial films Cd _x Hg_1–x Te for x ~ 0.2, with the initial electron concentration and mobility n = 10¹⁴ cm^-3 and μ = 2∙10⁵ cm²∙V^–1∙s^–1 is numerically simulated. The dependences of degree of reconstruction of the hole-concentration distribution profile on the depth of a shunting n-layer and magnitude of the magnetic field, at which the electrophysical parameters of the p ⁺–n structure are measured, are calculated. The dependence of the limiting magnetic field determining the magnetic-field range for measurements on the n-layer depth is found. It is shown that in calculations one should use the conduction values measured at the same magnetic fields as the Hall coefficients for determination of the holeconcentration distribution profile using the Petritz model.     

Single-ion approach to the interpretation of the x-ray photoelectron spectra of the valence bands of monoxides of 3d elements

The single-ion approach taking account of only the intra-atomic Coulomb interaction in free d ⁿ ions and in d ⁿ ions in an O _h crystal field is used to analyze the fine structure of the x-ray photoelectron spectra of the valence bands of monoxides of 3d elements. The x-ray photoelectron spectra were studied as a collection of d ⁿ⁻¹ and d ⁿ L multiplets representing the unscreened and screened parts, respectively, of the final state. The unscreened part of the final state can be described by the distribution of the line strengths of the photoelectronic transition d ⁿ → d ⁿ⁻¹ and the screened part can be described as a partially relaxed distribution of the statistical weights of the d ⁿ ions. Fiz. Tverd. Tela (St. Petersburg) 39, 1056–1063 (June 1997)     

Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =-Λ + w ₁ρ(a) + w ₂ a ^β + 0 and energy density ρ = Λ+ρ₀₁ a ^-3(1+w) +ρ₀₂ a ^α +ρ₀₃ a ^-3, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Ω_m,0 ≃ 0.4 and n ≃ -1 (β = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Ω_m,0 = 0.3 then the favoured model is close to concordance ΛCDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the ΛCDM model, while intermediate distant SNIa should be fainter than in the ΛCDM model. We also investigate whether the model with scaling fluid is actually preferred by data over ΛCDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The quenching of nucleon yields in the nonmesonic weak decay of Λ -hypernuclei and the three-body weak decay process

Recent exclusive coincidence measurements of non-mesonic weak decays (NMWD) reported for the ratio of the partial decay width of neutron-induced-to-proton-induced NMWD, Γ_n/Γ_p , values of 0.45±0.11±0.03 and 0.51±0.13±0.04 for 5lam and ¹² _Λ C , respectively. These observations agree well with the improved theoretical Γ_n/Γ_p ratios which are in the range of 0.3-0.7. It appears that the long-standing discrepancy between the experimental and theoretical values of Γ_n/Γ_p has finally been solved. However, when compared to the results of intra-nuclear cascade (INC) calculations, the observed numbers of both single nucleons and coincident nucleon pairs are strongly quenched. The quenching of the proton yield observed previously has been interpreted as an increase of the Γ_n/Γ_p ratio. On the other hand, significant contributions from the two-nucleon-induced three-body process ΛNN → nNN are predicted. Indeed, the angular correlation of the emitted nucleon pairs in the NMWD of ¹² _Λ C showed not only decay events in back-to-back kinematics, but also events with non-back-to-back kinematics. In this paper we show that the difficulties to extract the correct Γ_n/Γ_p ratio from the proton spectra is related to the three-body weak-interaction process which strongly quenches the nucleon yields.     

Mode field diameter and cut-off wavelength measurements of single mode optical fiber standards used in OTDR calibrations

This paper describes determination of the mode field diameter (MFD), and the cut-off wavelength of the single mode optical fiber standards used in OTDR calibrations, which was constructed in Optics Laboratory of National Metrology Institute of Turkey. Measurements of MFD were performed using computer controlled stepper motor unit with far field scanning (FFS) Method. For the same standard fibers, cut-off wavelength measurement was performed employing bend reference method, which is one of the transmitted power techniques. For both measurements, a nitrogen-cooled 5 mm InGaAs radiometer was used to detect optical flux. Detailed uncertainty analyses were presented for the MFD and cut-off measurements. While the total expanded uncertainties in MFD data at 1306.7 nm and 1550 nm were calculated as 0.8% and 1.0% (k=2), respectively, the total expanded uncertainty at determination of cut-off wavelength was found as 0.318% (k=2).     

Localization of Surface Spectra

We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H ₀), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ _d and Λ _d such that for |λ|<lambda; _d and |λ|> Λ _d the spectrum of H outside σ(H ₀) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999     

Snyder''s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ℓ _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ℓ _P /R ∼ 10⁻⁶¹.      

On Noncommutative Multi-Solitons

 We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ²) ^k /S _k . We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ²/ℤ _k , cylinder, and T ² . However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli space provides an explicit K?hler resolution of (ℝ⁴) ^k /S _k . In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ ^d , which for d>2 (and k>3) is not smooth and can have multiple branches. Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002 Communicated by R.H. Dijkgraaf     

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei _ΛΛ ⁶ He, _ΛΛ ¹⁰ Be, _ΛΛ ¹⁴ C, _ΛΛ ¹⁸ O, _ΛΛ ²² Ne, _ΛΛ ²⁶ Mg, _ΛΛ ³⁰ Si, _ΛΛ ³⁴ S, _ΛΛ ³⁸ Ar, _ΛΛ ⁴² Ca, _ΛΛ ⁴⁶ Ti, _ΛΛ ⁵⁰ Cr, _ΛΛ ⁵⁴ Fe, _ΛΛ ⁵⁸ Ni, _ΛΛ ⁶² Zn, _ΛΛ ⁶⁶ Ge, _ΛΛ ⁷⁰ Se, _ΛΛ ⁷⁴ Kr, _ΛΛ ⁷⁸ Sr, _ΛΛ ⁸² Zr, _ΛΛ ⁸⁶ Mo, _ΛΛ ⁹⁰ Ru, _ΛΛ ⁹⁴ Pd, _ΛΛ ⁹⁸ Cd, _ΛΛ ¹⁰² Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. _ΛΛ ⁶ He and _ΛΛ ¹⁰ Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly Λ-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for K _max=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

ΛN Space-exchange effects in thes-shell hypernuclei and Λ 9 Be

Variational Monte Carlo calculations of the ground state separation energiesB _Λ of thes-shell hypernuclei and also of _Λ ⁹ Be have been made for an Urbana-type central space-exchange ΛN potential consistent with Λp scattering, and also including three-body ΛNN forces. Thes-shell hypernuclei are treated asA-body systems (A = baryon number), and _Λ ⁹ Be is analysed as a partially nine-body problem in the Λ — 2α model. The reduction ofB _Λ due to the space-exchange ΛN potential has been calculated for thes-shell hypernuclei for a range of interactions: both ΛN and ΛN + ΛNN forces. ForA = 3,4,5 the exchange energy is approximately, 0.04, 0.15 and 0.50 MeV, respectively. For _Λ ⁹ Be a much more limited study gives ≅ 1.3 MeV. These values are much larger than that for ‘soft’ ΛN +NN potentials when the correlations are weak. Preliminary results were presented at the DAE Symp. on ‘Nuclear Physics’ Vol. 32B (1989).     

Cluster model of s- and p-shell ΛΛ hypernuclei

The ΛΛ binding energy (B _ΛΛ) of the s- and p-shell hypernuclei are calculated variationally in the cluster model and multidimensional integrations are performed using Monte Carlo. A variety of phenomenological Λ-core potentials consistent with the Λ-core energies and a wide range of simulated s-state ΛΛ potentials are taken as input. The B _ΛΛ of _ΛΛ⁶He is explained and _ΛΛ⁵He and _ΛΛ⁵H are predicted to be particle stable in the ΛΛ-core model. The results for s-shell hypernuclei are in excellent agreement with those of non-VMC calculations. The _ΛΛ¹⁰Be in ΛΛαα model is overbound for combinations of ΛΛ and Λα potentials. A phenomenological dispersive three-body force, V _Λαα, consistent with the B _Λ of _Λ⁹Be in the Λαα model underbinds _ΛΛ¹⁰Be. The incremental ΔB _ΛΛ values for the s- and p-shell cannot be reconciled, consistent with the finding of earlier analyses.      

Rare decays of Λb→Λ+γ and Λb→Λ+l+l? in the light-cone sum rules

The weak decays of Λ _b →Λ+γ and Λ _b →Λ+l ⁺ l ⁻ are investigated in the standard model using the light-cone sum-rule approach. The higher-twist distribution amplitudes of the Λ baryon to the leading conformal spin are included in the sum rules for the transition form factors. Our results indicate that the higher-twist distribution amplitudes almost have no influence on the transition form factor f ₂(q ²) defined by the tensor current, while such corrections can have a significant impact on the form factors g ₂(q ²) defined by a vector current. Two phenomenological models (COZ and FZOZ) for the wave function of the Λ baryon are also employed in the sum rules for comparison, which can give rise to form factors approximately five times larger than that in terms of conformal expansion. Utilizing the form factors calculated in LCSR, the physical observables like the decay rate, the polarization asymmetry and forward–backward asymmetry are analyzed for the decays of Λ _b →Λ γ, Λ l ⁺ l ⁻.     

Search for exotic baryons at HERMES

An experimental search for the Θ(1540)- and Λ(1520)-resonance was performed in quasi-real photoproduction on deuterium at the HERMES experiment. While evidence for Θ(1540) was found in the decay channel pK ⁰ _S→pπ ⁺ π ^-, no evidence for the corresponding anti-particle was found. In some models it is expected that the Θ(1540) and the Λ(1520) have similar production mechanisms. The photoproduction cross-sections for the Λ(1520) in the decay channel Λ(1520)→pK ^- and the corresponding anti-particle are determined. The partial photoproduction cross-sections for Λ(1520) and ˉ(1520) are obtained as σ _Λ(1520) = 65.3±8.8(stat)±6.9(syst)nb and σ _ˉ(1520) = 9.8±2.6(stat)±0.9(syst)nb, corresponding to a ratio R _Λ(1520) = σ _ˉ(1520)/σ _Λ(1520) = 0.15±0.05(stat)±0.02(syst).     

Realistic searches on stretched exponential networks

We consider navigation or search schemes on networks which have a degree distribution of the form P(k) ∝ exp(−k ^γ). In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter λ. The searches are realistic in the sense that not all search chains can be completed. An estimate of μ = ρ/s _d, where ρ is the success rate and s _d the dynamic path length, shows that for a network of N nodes, μ ∝ N ^−δ in general. Dynamic small world effect, i.e., δ ≃ 0 is shown to exist in a restricted region of the λ−γ plane.