Abstract We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations flow in, and deformation of, fractured materials. present models in both context of finite infinitesimal strain, discuss nonlinear (and non-differentiable) constitutive laws such as friction contact fracture. Using theory well-posedness evolutionary...

We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the lattice loop representation and showing that they have appropriate (singular) continuum limits and algebras. The diffeomorphism constraint reproduces the classica...

Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stre...

In this paper Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investi...

We show that, to all orders of powers of the gauge potential, a gauge anomaly A defined on 4-dimensional infinite lattice can always be removed by a local counterterm, provided that A depends smoothly and locally on the gauge potential and that A reproduces the gauge anomaly in the continuum theory in the classical continuum limit: The unique exception is proportional to the anomaly in the cont...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

It is well-known that the Interparticle interactions between adsorbates and surface of an adsorbent can affect the surface morphology. One of the consequences of this issue is that the resonant frequency of a nanoscale resonator can be changed due to adsorption. In this study we have chosen a cantilever-based nanoscale mass-sensor with a single nanoparticle at its tip. Using the classical...

This paper shows how to construct classical and quantum field C*-algebras modeling a $$U(1)^n$$ -gauge theory in any dimension using novel approach lattice gauge theory, while simultaneously constructing strict deformation quantization between the respective algebras. The construction starts with maps defined on operator systems (instead of C*-algebras) associated lattices, way that commutes al...