Given a singular modulus $j_0$ and set of rational primes $S$, we study the problem effectively determining moduli $j$ such that $j-j_0$ is an $S$-unit. For every $j_0 \neq 0$, provide effective way finding this for infinitely many choices $S$. The same true if $j_0=0$ assume Generalized Riemann Hypothesis. Certain numerical experiments will also lead to formulation "uniformity conjecture" $S$-...

Abstract Natural rocks are polymineral composites with complex microstructures. Such strong heterogeneities significantly affect the estimation of effective moduli by some theoretical models. First, we have compared isotropic predicted Kuster–Toksöz (KT) model and Mori–Tanaka (MT) model. The widely used KT only has finite precision in many cases because its assumption that is restricted to firs...

Seismic piezocone device (SCPTu) together with Resonant Column and Cyclic Triaxial test apparatus are employed to measure small strain shear modulus (G0) of carbonate sandy and clayey soils of southern coasts of Iran. A large area of southern regions of Iran is formed from clay, silt and sand. In this study, maximum shear modulus that is derived from both field (by seismic piezocone) and labora...

This paper is concerned with the effective piezoelectric moduli of a special class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the matrix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symmetry. The exact express...

Abstract Moduli potential loses its minima due to external energy sources of inflaton density or radiation produced at the end inflation. But, non-existence does not necessarily mean destabilization moduli. In fact, moduli is always dependent on initial field values fields. this work, we study carefully how effects reheating ease problem destabilization. The associated time scale produce therma...

We analyze the behaviour of moduli fields in string effective models between the end of inflation and reheating. The effective moduli potential during this era is derived for a class of simple models. We argue that this potential significantly stabilizes the modulus at its high energy minimum, if some restrictions on modular weights are met. Two mechanisms to further stabilize the moduli to the...