Alternating quaternary algebra structures on irreducible representations of sl(2,C)

We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power $\Lambda^4 V(n)$. The multiplicity is 1 (resp. 2) if and only if n = 4, 6 (resp. n = 8, 10). For these n we determine the multilinear polynomial identities of degree $\le 7$ satisfied by the sl(2,C)-invariant alternating quaternary algebra structures obtained from the projections $\Lambda^4 V(n) \to V(n)$. We represent the polynomial identities as the nullspace of a large integer matrix and use computational linear algebra to find the canonical basis of the nullspace.Comment: 26 pages, 13 table

The growth dynamics of the wedding-cake Interfaces

In the limit where the ratio of the surfaces diffusion coefficient to the deposition rate D/F ∞ → , the surface consists of wedding-cake structures. In order to understand the growth dynamics and the scaling properties of theses interfaces, we have calculated the time evolution of its width ω(L,t) for both one and two dimensional lattice. By the use of the dynamic scaling approach, we find that ω(L,t) scales with time t and length L as ω(L,t)≈Lα f(t/Lα/β ) where f is a scaling function and α and β are respectively the roughening and the growth exponents. The values of theses exponents are in good agreement with the theoritical ones predicted by the Edwards-Wilkinson equation.In the limit where the ratio of the surfaces diffusion coefficient to the deposition rate D/F ∞ → , the surface consists of wedding-cake structures. In order to understand the growth dynamics and the scaling properties of theses interfaces, we have calculated the time evolution of its width ω(L,t) for both one and two dimensional lattice. By the use of the dynamic scaling approach, we find that ω(L,t) scales with time t and length L as ω(L,t)≈Lα f(t/Lα/β ) where f is a scaling function and α and β are respectively the roughening and the growth exponents. The values of theses exponents are in good agreement with the theoritical ones predicted by the Edwards-Wilkinson equation

Temporal fluctuations of current surface density in a triangular lattice

In this paper, we examine the effect of the temporal fluctuation current correlation in the surface diffusion process in a triangular lattice, in the framework of the lattice gas model. Our calculations are per found in small circular surfaces equivalent to the probe areas in the scanning microscopy experiments. We have found that the correlation function, in the non- interacting case, follows the law Öp . In the presence of repulsive interactions between mobile particles, it behaves like Öp exp(8γp). We have also calculated the collective diffusion coefficient by the linear response theory and by the characteristic time method, which reflect clearly the order-disorder effect on the diffusion.In this paper, we examine the effect of the temporal fluctuation current correlation in the surface diffusion process in a triangular lattice, in the framework of the lattice gas model. Our calculations are per found in small circular surfaces equivalent to the probe areas in the scanning microscopy experiments. We have found that the correlation function, in the non- interacting case, follows the law Öp . In the presence of repulsive interactions between mobile particles, it behaves like Öp exp(8γp). We have also calculated the collective diffusion coefficient by the linear response theory and by the characteristic time method, which reflect clearly the order-disorder effect on the diffusion

Study of crack diffusion in composite materials using the fiber bundle model

Our aim is to investigate the crack diffusion created at single region of composite materials by using the fiber bundle model. So, we have applied an external single crack in one fiber of the composite material, and we then continue to increase this load at a very slow rate until the considered fiber breaks and its load is redistributed to its neighboring intact ones. This breaking and redistribution dynamics repeat itself and this process ensures an advancing interfacial fracture and the area of the damaged region increases with time until a final crack of material. Our calculations are done in the context of the local load-sharing rule. The results show that the damaged region area increases with time by following the Lifshitz-Slyozof law with an exponent growth x=2. This permits us to deduce the behavior of the crack diffusion with the applied load. The corresponding results of the life time materials exhibit an exponential decreasing with the applied load and a linear decreasing with temperature

Study of adatoms diffusion through current density fluctuation functions

In this work, we investigate the diffusion process by using a mean field lattice gas dynamical model. The temporal correlation function of the current density is calculated in a probe area of radius R. The latter is considered to test if the developed formulation can be applied to reproduce STM experiments. The obtained results concerning the effective diffusion coefficient exhibit clearly the order disorder transition effect translated by two minima appearing respectively at p=1/3 and p=2/3. The effect of the ordering phase at p=1/3 requires a threshold size more precisely, the minimum size system where, the ordering phase effect begins, to appear here is R=5.In this work, we investigate the diffusion process by using a mean field lattice gas dynamical model. The temporal correlation function of the current density is calculated in a probe area of radius R. The latter is considered to test if the developed formulation can be applied to reproduce STM experiments. The obtained results concerning the effective diffusion coefficient exhibit clearly the order disorder transition effect translated by two minima appearing respectively at p=1/3 and p=2/3. The effect of the ordering phase at p=1/3 requires a threshold size more precisely, the minimum size system where, the ordering phase effect begins, to appear here is R=5