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We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…

Hypothesis: Immiscible liquids are commonly used to achieve unique functions in many applications, where the breakup of compound droplets in airflow is an important process. Due to the existence of the liquid-liquid interface, compound…

Atomic collapse is a phenomenon inherent to relativistic quantum mechanics where electron states dive in the positron continuum for highly charged nuclei. This phenomenon was recently observed in graphene. Here we investigate a novel…

We consider a lattice model for three-component systems in which the lattice bonds are covered by molecules of type AA, BB, and AB, and the only interactions are between the molecular ends of a common lattice site. The model is equivalent…

Clusters of polycyclic aromatic hydrocarbon (PAH) molecules are modelled using explicit all-atom potentials using a rigid body approximation. The PAH's considered range from pyrene (C10H8) to circumcoronene (C54H18), and clusters containing…

A number of recent experimental studies have shown that solid-state complex organic molecules (COMs) can form under conditions that are relevant to the CO freeze-out stage in dense clouds. In this work, we show that alcohols can be formed…

We investigate the aggregation number and size distributions for inter-molecular clusters of amphiphilic diblock and triblock copolymers in poor solvent at very low concentrations. Diblocks and triblocks with hydrophilic ends are shown to…

We give the description of three-dimensional Lie triple systems and their corresponding Lie algebras with invomorphisme, The description of three-dimensional Bol algebras linked with the distinguished Lie triple systems above is given. The…

Given a compact oriented triangulated $3$-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used…

We have investigated the hydrogen-bonded structures in liquid methanol and a 7:3 mole fraction aqueous solution using classical Molecular Dynamics simulations at 298K and ambient pressure. We find that, in contrast to recent predictions…

Binary mixtures of two dimensional, site-based models of alcohols are investigated by computer simulations, with a focus on ideal mixing, local clustering and miscibility trends. Four representative systems are considered: methanol/ethanol,…

The structures of equimolar mixtures of the commonly used polar aprotic solvents dimethylformamide (DMF) and dimethylacetamide (DMAc) in dimethylsulfoxide (DMSO) have been investigated via neutron diffraction augmented by extensive…

Nature is remarkably adept at using interfaces to build structures, encapsulate reagents, and regulate biological processes. Inspired by Nature, we describe flexible polymer-based ribbons, termed "mesoscale polymers" (MSPs), to modulate…

We compute the integral cohomology rings of a family of 3-groups. As a corollary, we exhibit, for each n greater than or equal to 5, a pair of groups of order 3^n whose integral cohomology rings are isomorphic.

We calculate the mod-two cohomology of all alternating groups together, with both cup and transfer product structures, which in particular determines the additive structure and ring structure of the cohomology of individual groups. We show…

A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…

This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a…

It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there…

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…

We present a result on the number of decoupled molecules for systems binding two different types of ligands. In the case of $n$ and $2$ binding sites respectively, we show that, generically, there are $2(n!)^{2}$ decoupled molecules with…