相关论文: Tensegrities on the space of generic functions
In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditions of at most $(d+1)$-valent tensegrities in $\mathbb{R}^d$…
In this paper we formulate and prove necessary and sufficient geometric conditions for existence of generic tensegrities in the plane for arbitrary graphs. The conditions are written in terms of "meet-join" relations for the configuration…
We prove an equilibrium stressability criterium for trivalent multidimensional tensegrities. The criterium appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete…
We set new dual problems for the weighted spaces of holomorphic functions of one variable in domains on the complex plane, namely: nontriviallity of a given space, description of zero sets, description of (non-)uniqueness sets, the…
The fundamental ideas and tools of the global geometric formulation of stress and hyper-stress theory of continuum mechanics are introduced. The proposed framework is the infinite dimensional counterpart of statics of systems having finite…
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
In this paper, we introduce new classes of infinite and combinatorially periodic tensegrities, derived from algebraic multidimensional continued fractions in the sense of F. Klein. We describe the stress coefficients on edges through…
We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize…
In this paper the Feynman Green function for Maxwell's theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing…
The actions of the ``$R=T$'' and string-inspired theories of gravity in (1+1) dimensions are generalized into one single action which is characterized by two functions. We discuss differing interpretations of the matter stress-energy…
In 1864, J. C. Maxwell introduced a link between self-stressed frameworks in the plane and piecewise linear liftings to 3-space. This connection has found numerous applications in areas such as discrete geometry, control theory and…
In this paper we study the stressability of semi-discrete frameworks in the plane which are generated by a discrete sequence of smooth curves. We characterize their stressability property by the existence of stresses fulfilling certain…
One of the most influential early works in graphic statics is one of Maxwell, where he introduced the idea of a discontinuous stress function and the use of a 3D projective polarity for a planar problem. A recent work gave an analytical…
A fundamental element of scale-dependent gravity is the scale-setting procedure. We present a new covariant expression to set the scale that arises when examining the field equations. Considering the renormalization group equations and…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We show how a $d$-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) $d$-manifold in \rd naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
A stochastic theory of gravity is described in which the metric tensor is a random variable such that the spacetime manifold is a fluctuating physical system at a certain length scale. A general formalism is described for calculating…
We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms…
The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order…