Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

Isospin violations in largeP T pion inclusive processes in perturbative quantum chromodynamics

We investigate the asymmetries arising due to electromagnetic interactions in largeP _T pion inclusive processes. The hardqcd processes that contribute to such asymmetries areq+g→q+γ,q+q→g+γ etc. which are suspected to be substantial, as indicated by theqcd predictions for a significant and increasingγ/π ^o ratio at largeP _T. We calculate the expected isospin related asymmetries and propose tests that might detect them. Our estimates indicate that the effects are much smaller than may be naively expected. We also observe a remarkable scaling of asymmetries in the variableP _T/(s)^1/2.     

Dynamic Critical Behavior of the Chayes–Machta Algorithm for the Random-Cluster Model,I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes–Machta dynamics for the Fortuin–Kasteleyn random-cluster model, which generalizes the Swendsen–Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 1024², and obtain estimates for the dynamic critical exponent z _CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z _CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z _CM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.     

Radiative energy loss of high-energy quarks in finite-size nuclear matter and quark-gluon plasma

The induced gluon radiation of a high-energy quark in a finite-size QCD medium is studied. For a sufficiently energetic quark produced inside a medium we find the radiative energy loss ΔE _q∝L ², where L is the distance traveled by quark in the medium. It has a weak dependence on the initial quark energy E _q. The L ² dependence turns to L ¹ as the quark energy decreases. Numerical calculations are performed for a cold nuclear matter and a hot quark-gluon plasma. For a quark incident on a nucleus we predict ΔE _q ≈0.1E _q (L/10fm) ^β , with β close to unity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 585–589 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

Λ(1405) as a multiquark state

In the QCD sum rule approach we predict the Λ (1405) mass by choosing the π⁰Σ⁰ multiquark interpolating field. It is found that the mass is about 1.419 GeV from Π₁ (q ²) sum rule which is more reliable than Π_q (q ²) sum rule, where Π_q (q ²) and Π₁ (q ²) are two invariant functions of the correlator Π (q ²). We also present the sum rules for the K ⁺ p and the π⁺Σ⁺ multiquark states, and compare to those for the π⁰Σ⁰ multiquark state. The mass of the Λ (1600) can be also reproduced in our approach. Received: 11 November 1997 / Revised version: 28 April 1998     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work [1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R ₀, R ₁], R ₀ > 0, satisfies R ₁/R ₀ < 1/4. Moreover, given a sequence of solutions such that R ₁/R ₀ → 1, then the limit supremum of 2M/R ₁ was shown to be bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In this paper we show that the hypothesis that R ₁/R ₀ → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R ₁ is bounded, but that the limit is ((2Ω + 1)² − 1)/(2Ω + 1)² = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R ₁ arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R ₁ of any static solution of the spherically symmetric Einstein-Vlasov system.     

Cluster ion emission from LiF induced by MeV N<Superscript>q+</Superscript> projectiles and <Superscript>252</Superscript>Cf fission fragments

Ion cluster desorption yields from LiF were measured at PUC-Rio with ≈0.1 MeV/u N ^q+ (q = 2,4,5,6) ion beams by means of a time-of-fight (TOF) mass spectrometer. A ²⁵²Cf source mounted in the irradiation chamber allows immediate comparison of cluster emissions induced by ≈65 MeV fission fragments (FF). Emission of (LiF) _n Li⁺ clusters are observed for both the N beams and the ²⁵²Cf fission fragments. The observed cluster size n varies from 1 to 6 for N ^q+ projectiles and from 1 to ≈40 for the ²⁵²Cf-FF. The size dependence of the Y(n) distributions suggests two cluster formation regimes: (i) recombination process in the outgoing gas phase after impact and (ii) emission of pre-formed clusters from the periphery of the impact site. The corresponding distribution of ejected negative cluster ions (LiF) _n F⁻ closely resembles that of the positive secondary (LiF) _n Li⁺ ions. The desorption yields of positive ions scale as Y(n) ∼ q ⁵. A calculation with the CASP code shows that this corresponds to a cubic scaling ∼S _e ³ with the electronic stopping power S _e , as predicted by collective shock wave models for sputtering and models involving multiple excitons (Frenkel pair sputtering). We discuss possible interpretations of the functional dependence of the evolution of the cluster emission yield Y(n) with cluster size n, fitted by a number of statistical distributions.     

Noncommutative Instantons on the 4-Sphere¶from Quantum Groups

We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?⁷→?⁴ making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SU _q (2); it determines a new deformation of the 4-sphere ∑⁴ _q as the algebra of coinvariants in ? _q ⁷. We show that the quantum vector bundle associated to the fundamental corepresentation of SU _q (2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑⁴ _q , we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Received: 3 January 2001 / Accepted: 14 November 2001     

On the envelope soliton near critical density in a plasma with cold ions and two-temperature electrons

Summary We have analysed the formation of envelope soliton near critical density in a plasma consisting of two-temperature electrons and cold ions. The non-linear Schr?dinger-like equation obtained isiφ _t +pφ _xx +q|φ|⁴φ=0 which we call the modified non-linear Schr?dinger equation. It is also observed that this approach leads to a physical situation where a linear combination of both the modified and usual NLS equations holds, in the formiφ _t +pφ _xx +q ₁|φ|²φ +q ₂|φ|⁴φ=0. It is demonstrated through graphical analysis thatq ₁,q ₂, thought of as a function of β(=T _el/T _eh), behave in opposite way. That is, whenq ₁ grows,q ₂ decays, or vice versa. Lastly we demonstrate that this equation can sustain a type of solution other than the usual solitary profile. The form of such a wave is also depicted graphically.     

q 2-convolution and itsq 2-Fourier transform

The functions on the lattice generated by the integer degrees ofq ² are considered, 0<q<1. Theq ²-shift operator is defined. The multiplicators and theq ²-convolutors are defined in the functional spaces which are dual with respect to theq ²-Fourier transform. Theq ²-analog of convolution of twoq ²-distributions is constructed. Theq ²-analog of an arbitrary order derivative is introduced. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. The author was supported in part by the Russian Foundation for Fundamental Research (grant no. 0001-00143) and the NIOKR MPS RF     

Improvement of perturbation theory in QCD for e + e − →hadrons and the problem of α s freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q ²), corresponding to the process e ⁺ e ⁻→ hadrons, is considered in detail. By the use of the analytical properties of Π(q ²) and a perturbation expansion of Π(q ²) for q ²<0, the function ImΠ(q ²) at q ²>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q ²)=σ(e ⁺ e ⁻ →hadrons)/(e ⁺ e ⁻→μ ⁺ μ ⁻) is improved. After substitution of R(q ²) into the dispersion relation an improved Adler function D(q ²) is obtained, having no infrared pole and a frozen α _s (q ²). Good agreement with experiment is achieved. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Vibrational Feshbach resonances in electron attachment to carbon dioxide clusters

Using a high resolution ( meV) laser photoelectron attachment method, we have studied the formation of (CO ₂) _q ⁻ ions (q = 4−22) in collisions of low energy electrons (1−180 meV) with (CO₂) _N () clusters. The previously reported “zero energy resonance”, observed at much larger electron bandwidths, actually consists of several narrow vibrational Feshbach resonances of the type [(CO ₂) _{N −1}CO which involve a vibrationally-excited molecular constituent ( denotes vibrational mode) and a diffuse electron weakly bound to the cluster by long range forces. The resonances occur at energies below those of the vibrational excitation energies of the neutral clusters [(CO ₂) _{N −1}CO ]; the redshift rises with increasing cluster ion size q by about 12 meV per unit; these findings are recovered by a simple model calculation for the size dependent binding energies. The size distribution in the cluster anion mass spectrum, resulting from attachment of very slow electrons, mainly reflects the amount of overlap of solvation-shifted vibrational resonances with zero energy; the cluster anion size q is identical with or close to that of the attaching neutral cluster. Received 11 January 2000 and Received in final form 10 April 2000     

Twisted Covariance as a Non-Invariant Restriction of the Fully Covariant DFR Model

We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_q^m,q_qⁿ]=iq^mn{[q_\theta^\mu,q_\theta^\nu]=i\theta^{\mu\nu}} , where the matrix θ is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists.     

Electron yield per ion charge-state correction for an ion collector with unsuppressed secondary electron emission

The electron yield per ion charge-state γ/q was measured for emission of electrons from clean polycrystalline gold induced due to impact of Ta ^q+ (11≤q≤41) ions with kinetic energy per chargeE _i/q from 15 keV/q to 150 keV/q. The dependence of γ on angle of incidence was analyzed with use of relation γ(ϑ)=γ₀ cos^−f ϑ. The fitting of experimental data gives a range of γ₀/q from 1 to 1.75 for Ta¹³⁺ and from 1.5 to 1.73 for Ta³⁹⁺. The dependence of γ₀/q onq andE _i is discussed with respect to measurement of ion currents emitted from laser-produced plasmas with an ion collector with unsuppressed secondary electron emission. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy, and by grant A1010819 from the Grant Agency of the Academy of Sciences of the Czech Republic.     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.     

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 ⁻.     

Geometrical Tools for Quantum Euclidean Spaces

We apply one of the formalisms of noncommutative geometry to ℝ ^N _q , the quantum space covariant under the quantum group SO _q (N). Over ℝ ^N _q there are two SO _q (N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of ℝ³ _q . As in the case N=3, one has to slightly enlarge the algebra ℝ ^N _q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ ^N _q . While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ ^N _q with U _q so(N) into ℝ ^N _q , an interesting result in itself. Received: 4 March 2000 / Accepted: 11 October 2000     

The β function,scaling, and improved action forSU(3) lattice gauge theory

We present a detailed analysis of the nonperturbativeβ function along the Wilson axis for theSU(3) pure gauge theory using the Monte Carlo renormalization group method. The scaling behavior of the string tension, the deconfinement transition temperature, and the O⁺⁺ glueball mass obtained from published data is compared. The results show that there is no asymptotic scaling forK _F=(6/g ²)<6.1. We also estimate the renormalized action generated by the √3 block transformation for use in future calculations.