Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

Determination of nickel in natural waters by FAAS after sorption on octadecyl silica membrane disks modified with a recently synthesized Schiff's base

A simple, highly sensitive, accurate and selective method for the determination of trace amounts of Ni²⁺ ions in water samples is proposed. The method is based on the separation and preconcentration of Ni²⁺ on an octadecyl-bonded silica (ODBS) membrane disk modified by a recently synthesized Schiff’s base N,N′-bis (3-methylsalicylidene) ortho phenylene diamine (MSOPD) at pH 7. The synthesis of this extractant ligand is also described. The retained nickel on the membrane was eluted with 2×5 ml 0.5 M HNO₃ and measured by flame atomic absorption spectrometry (FAAS) at 232.0 nm. The extraction efficiency and the influence of the type and least amount of eluent for the stripping of Ni²⁺ from the disks, pH, flow rates of sample solution and eluent, amount of MSOPD, effect of other ions, and breakthrough volume were evaluated. The maximum capacity of the membrane disks modified by 3 mg of MSOPD was found to be 146±4 μg Ni²⁺. The 3σ limit of detection of the method was 30 ng per 1000 ml and also an enrichment factor of 250 was obtained. The proposed method has been applied to the determination of nickel in several water samples with satisfactory results.     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Exactly solvable reaction diffusion models on a Cayley tree

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.     

Phase transitions of large-N two-dimensional Yang–Mills and generalized Yang–Mills theories in the double scaling limit

The large-N behavior of Yang–Mills and generalized Yang–Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function of N. It is shown that phase transitions of different orders occur, depending on the functional dependence of the area on N. The finite-size scalings of the system are also investigated. Specifically, the dependence of the dominant representation on A, for large but finite N is determined.     

Greens functions of 2-dimensional Yang-Mills theories on nonorientable surfaces

By using the path integral method, we calculate the Green functions of the field strength of Yang-Mills theories on arbitrary nonorientable surfaces in Schwinger-Fock gauge.We show that the non-gauge invariant correlators consist of a free part and an almost x-independent part. We also show that the gauge invariant n-point functions are those corresponding to the free part, as in the case of orientable surfaces.     

Solid-phase Extraction and High Performance Liquid Chromatographic Determination of Folic Acid in Fortified Foodstuffs: a Recommended Process Utilizing a New Strong Anion Exchange Sorbent

Journal of Analytical Chemistry - A highly efficient solid-phase extraction (SPE) column filled with a silica-based strong anion exchange sorbent was reported in the current study. The fabricated...     

Exact Determination of the Phase Structure of a Multi-Species Asymmetric Exclusion Process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two-phase regime. In the three-phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high-density phase.     

Anisotropic Heisenberg Magnet with Long-Range Interactions. Integrability and Phase Structure

We show that the xxz Heisenberg magnet withlong-range interactions in a magnetic field, isintegrable both classically and quantum mechanically.Explicit expressions are given for the involutiveintegrals of the motion. The nature of the spectrum andthe ground state are clarified and the partitionfunction is calculated exactly in the thermodynamiclimit. A detailed study of the phase structure of thesystem is also performed.