We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence functional resembles that of the continuum theory but the counterpart of the d’Alembertian operator is nonlocal and a generalized inverse of the discrete retarded Green function. We comment on the significance of this and w...

The lateral free vibration of micro-rods initially subjected to axial loads based on a nonlocal continuum theory is considered. effects long-range interaction fields the natural frequencies and modes are examined. A simply supported micro-rod taken as an example; linear responses observed by two different methods, including separation variables multiple scales analysis. relations between mode d...

In this paper, mechanics of continuum with general form nonlocality in space and time is considered. Some basic concepts nonlocal are discussed. General fractional calculus (GFC) vector (GFVC) used as mathematical tools for constructing media time. Balance equations mass, momentum, energy, which describe conservation laws continuum, derived by using the fundamental theorems GFC. The balance equ...

This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. Using doublet mechanics, the relation between natural f...

From its early days the SPH method has been criticised for shortcomings namely tensile instability and consistency. Without thorough understanding of attempts were made to make classical consistent stable which resulted in local Total Lagrangian forms similar finite element method. In this paper we derived analysed a nonlocal similarity with Bazant’s imbricate continuum. addition, provides comp...

In the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytic...

The classic localization instability analysis for strain-softening materials is expanded to dynamic solutions. The nonlocal continuum with local strain, which ensures proper convergence of finite element calculations and physically realistic solutions, is adopted in its simplified form, the nonlocal damage model. The dynamic response of a one-dimensional bar initially in a uniform strain-soften...

Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect ...