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.     

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     

l-Proline-catalysed one-pot synthesis of tetrahydrobenzo[c]acridin-8(7H)-ones at room temperature

Only 10 mol% of l-Proline in ethanol proved to be a very efficient catalyst for the one-pot synthesis of a wide variety of highly substituted tetrahydrobenzo[c]acridin-8(7H)-ones at room temperature. The key advantages of this process are high yields, cost effectiveness of the catalyst, easy work-up and the products can be directly recrystallized from hot ethanol.     

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.     

Constraining chameleon field driven warm inflation with Planck 2018 data

The European Physical Journal C - We study the Yukawa model with one scalar and one axial scalar fields, coupled to N copies of Dirac fermions, in curved spacetime background. The theory possesses...     

Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of correlation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superautonomous models, a nonuniform voter model is introduced, and solved explicitly.     

Coated wire ion-selective electrode for palladium(II) and its application to catalyst analysis

The construction, performance and application of polymeric membrane (PME) and coated wire (CWE) palladium(II)-selective electrodes based on the ion pair between tetra bromopalladate(II) and hexadecylpyridinium cation (HDP⁺) in a poly(vinyl chloride) matrix, plasticized with o-NPOE are described. The influence of membrane composition, bromide ion concentration and pH on the potentiometric responses of electrodes were investigated. Nernstian responses were obtained for the two type of electrodes with low limits of detection (1.0×10⁻⁶ M for PME and 5.0×10⁻⁸ M for CWE). The potentiometric responses are independent of the pH of test solution in the range 3–8. The response time of electrodes are fast (30 s for PME and 10 s for CWE), and they can be used for at least 3 months without any considerable divergence in potentials. The proposed electrodes revealed good selectivity for palladium(II) respect to different cations and anions. They were used to the direct potentiometric determination of palladium(II) in silicon-alumina catalysts.     

One-dimensional Kinetic Ising Model with Nonuniform Coupling Constants

A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. The static behavior of the system is investigated. It is shown that there are cases where the system exhibits a static phase transition, which is a change of behavior of the static profile of the expectation values of the spins near end points.