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Dimension D (dimension + d)
Selected AbstractsDynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogelsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5-1 2010Dimas R. Vollet Dynamical scaling properties in fractal structures were investigated from small-angle X-ray scattering (SAXS) data of the kinetics of aggregation in silica-based gelling systems. For lack of a maximum in the SAXS intensity curves, a characteristic correlation distance , was evaluated by fitting a particle scattering factor model valid for polydisperse coils of linear chains and f -functional branched polycondensates in solution, so the intensity at q = ,,1, I(,,1, t), was considered to probe dynamical scaling properties. The following properties have been found: (i) the SAXS intensities corresponding to different times t, I(q, t), are given by a time-independent function F(q,) = I(q, t),,D/Q, where the scattering invariant Q has been found to be time-independent; (ii) , exhibited a power-law behavior with time as ,,t,, the exponent , being close to 1 but diminishing with temperature; (iii) I(,,1, t) exhibited a time dependence given by I(,,1, t) ,t,, with the exponent , found to be around 2 but diminishing with temperature, following the same behavior as the exponent ,. In all cases, ,/, was quite close to the fractal dimension D at the end of the studied process. This set of findings is in notable agreement with the dynamical scaling properties. [source] Modifications in the correlation function in poly(vinyl alcohol)/silica hybrid wet gelsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2009Dimas R. Vollet Small-angle X-ray scattering was used to study structural modifications in tetraethoxysilane-derived poly(vinyl alcohol) (PVA)/silica hybrids. The basic structure of the wet gels can be described as a mass-fractal structure with fractal dimension D equal to 2 and characteristic length ,, which increases with addition of PVA. Wet gels with high PVA content exhibit a positive deviation from the mass-fractal power-law scattering at low q; this deviation is associated with additional scattering due to a second large correlation distance ,, reinforced by the addition of PVA. The fraction of both contributions to the total correlation function was estimated; this is the first time that such a study has been carried out for mass-fractal structures. [source] Polymer hydration and microphase decomposition in poly(N -vinylcaprolactam),water complexJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2003Vassili Lebedev Poly(N -vinylcaprolactam) (PVCL) is a synthetic analogue of biomolecules (enzymes, proteins). It demonstrates a specific hydration and undergoes a coil,globule transition. The PVCL,D2O system (PVCL mass M = 106) has been investigated by small-angle neutron scattering (SANS) at T = 296,316,K to identify the structural features of the collapse at concentration C = 0.5,wt% near the threshold of the coil overlap. (The collapse leads to the segregation of the phase enriched with polymer at T > 305,K). The SANS experiments at q = 0.1,5,nm,1 (scales from monomer unit to globule gyration radius RG, 16,nm) have revealed a stretched coil,globule transformation in the range 305,309,K. Using high-resolution SANS (q = 0.002,0.02 nm,1) the globule association to form fractal structures (sponge-like) of surface dimension DF, 2.4,2.6 was examined. The coexistence of globules and disordered chains (regions ,5,10,nm) was found. The growth of the content of globular phase was induced by the conformational transition in disordered molecular fragments from coiled (dimension D, 1.8) to stretched chains (D, 1.2). [source] Hard-to-Solve Bimatrix GamesECONOMETRICA, Issue 2 2006Rahul Savani The Lemke,Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d -space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke,Howson computations, finding an equilibrium by support enumeration takes on average exponential time. [source] Higher-dimensional point groups in superspace crystallographyACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2008A. Janner Crystallographic puzzles not covered by the present crystallography, like integral indexing and crystallographic scaling of axial-symmetric biomacromolecules and icosahedral viral capsids and/or integral lattices, can possibly be explained by extending (n,d)-dimensional superspace crystallography to include finite subgroups of the higher-dimensional orthogonal group O(n) and not only those of O(d), as restricted by the physical dimension d. [source] A randomized clinical trial of strength training in young people with cerebral palsyDEVELOPMENTAL MEDICINE & CHILD NEUROLOGY, Issue 10 2003Karen J Dodd PhD This randomized clinical trial evaluated the effects of a home-based, six-week strength-training programme on lower limb strength and physical activity of 21 young people (11 females, 10 males; mean age 13 years 1 month, SD 3 years 1 month; range 8 to 18 years) with spastic diplegic cerebral palsy (CP) with independent ambulation, with or without gait aids; (Gross Motor Function Classification System levels I to III). Compared with the 10 controls, the 11 participants in the strength-training programme increased their lower limb strength (combined ankle plantarflexor and knee extensor strength as measured by a hand-held dynamometer) at 6 weeks (F(1,19)=4.58, p=0.046) and at a follow-up 12 weeks later (F(1,18)=6.25, p=0.041). At 6 weeks, trends were also evident for improved scores in Gross Motor Function Measure dimensions D and E for standing, running and jumping, and faster stair climbing. A relatively short clinically feasible home-based training programme can lead to lasting changes in the strength of key lower-limb muscles that may impact on the daily function of young people with CP. [source] Adults with cerebral palsy: walking ability after progressive strength trainingDEVELOPMENTAL MEDICINE & CHILD NEUROLOGY, Issue 4 2003C Andersson MSc PT The purpose of this study was to evaluate effects of a progressive strength training programme on walking ability in adults with cerebral palsy. Ten individuals with spastic diplegia (seven males, three females; mean age 31, range 23,44 years) participated twice a week over 10 weeks. Seven individuals with spastic diplegia (four males, three females; mean age 33, range 25,47 years) who did not receive strength training served as controls. All individuals were ambulatory but motor ability ranged from functional walkers to individuals who always required walking aids and used a wheelchair regularly. Significant improvements were seen in isometric strength (hip extensorsp=0.006, hip abductors p=0.01), and in isokinetic concentric work at 30/s (knee extensors p=0.02) but not in eccentric work. Results also showed significant improvements in Gross Motor Function Measure (GMFM) dimensions D and E (p=0.005), walking velocity (p=0.005), and Timed Up and Go (p=0.01). There was no increase in spasticity for those who underwent strength training. Individuals in the control group did not show any significant improvement in any measured variable. The groups were small, however, and there was no significant difference between the groups in any measured variable. These findings suggest that a 10-week progressive strength training programme improves muscle strength and walking ability without increasing spasticity. [source] Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phasesANNALEN DER PHYSIK, Issue 9 2009K. Byczuk Abstract We derive a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose-Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF-DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one-half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions. [source] Percolation for the vacant set of random interlacementsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2009Vladas Sidoravicius We investigate random interlacements on ,d, d , 3. This model, recently introduced in [8], corresponds to a Poisson cloud on the space of doubly infinite trajectories modulo time shift tending to infinity at positive and negative infinite times. A nonnegative parameter u measures how many trajectories enter the picture. Our main interest lies in the percolative properties of the vacant set left by random interlacements at level u. We show that for all d , 3 the vacant set at level u percolates when u is small. This solves an open problem of [8], where this fact has only been established when d , 7. It also completes the proof of the nondegeneracy in all dimensions d , 3 of the critical parameter u* of [8]. © 2008 Wiley Periodicals, Inc. [source] | ||||||||||