相关论文: Mathematical Foundations of Interlocking Assemblie…
Hierarchical self-assembly consisting of local associations of simple building-blocks for the formation of complex structures widely exists in nature, while the essential role of local assembly remains unknown. In this work, by using…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…
Proteinaceous aggregation occurs through self-assembly-- a process not entirely understood. In a recent article [1], an analytical theory for amyloid fibril growth via secondary rather than primary nucleation was presented. Remarkably, with…
Soft composite solids are made of inclusions dispersed within soft matrices. They are ubiquitous in nature and form the basis of many biological tissues. In the field of materials science, synthetic soft composites are promising candidates…
Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
We characterise finite and infinitesimal rigidity for bar-joint frameworks in R^d with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be…
In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of…
In this paper, we consider folding assembly as an assembly primitive suitable for dual-arm robotic assembly, that can be integrated in a higher level assembly strategy. The system composed by two pieces in contact is modelled as an…
We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons and fermions. In each case properties of an entanglement measures are related to the decomposition of the suitably chosen representation of the…
We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…
By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…
This paper finds relationships between multiple logarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin's R-deco polygon representation of multiple logarithms to find…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they…
Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space…
Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of interval-closed sets of finite posets from enumerative and dynamical perspectives. In particular, we use the generalized toggle group to define…