Evaluation of an Asphalt Mixture Containing a High Content of Reclaimed Asphalt and Different Crumb Rubber Modified Binders

Recently, environmental concerns have become a primary driving force in most countries and industries dealing with natural resources. As a part of this category, asphalt pavement industry is trying to implement more green and sustainable features in its products, while maintaining the mechanical and performance-based properties of the resulting asphalt mixtures. Among potential recycled materials, vehicle tires and aged asphalt pavement have been demonstrated to show economic, ecological, and behavioral improvements in the mixtures. However, mixtures with a high content of reclaimed asphalt (RA) and crumb rubber present some limitations. Therefore, using another group of additives, i.e., a warm mix asphalt (WMA) additive, has been considered. The presented paper investigates the use of an elevated content of RA with different crumb rubber modified binders and (in some mixtures) a warm mix additive in an asphalt concrete (AC) binder mix. Regular empirical tests have been conducted and more advanced performance or functional characteristics, i.e., stiffness, thermal induced cracking, resistance to permanent deformation, complex modulus have been determined and evaluated. Selected results are presented in the paper.

Classification of universal formality maps for quantizations of Lie bialgebras

We settle several fundamental questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. Moreover, we settle these questions in a greater generality: we give a complete classification of the associated universal formality maps. An important new technical ingredient introduced in this paper is a polydifferential endofunctor ${\mathcal {D}}$ in the category of augmented props with the property that for any representation of a prop ${\mathcal {P}}$ in a vector space $V$ the associated prop ${\mathcal {D}}{\mathcal {P}}$ admits an induced representation on the graded commutative algebra $\odot ^\bullet V$ given in terms of polydifferential operators. Applying this functor to the minimal resolution $\widehat {\mathcal {L}\textit{ieb}}_\infty$ of the genus completed prop $\widehat {\mathcal {L}\textit{ieb}}$ of Lie bialgebras we show that universal formality maps for quantizations of Lie bialgebras are in one-to-one correspondence with morphisms of dg props \[F: \mathcal{A}\textit{ssb}_\infty \longrightarrow {\mathcal{D}}\widehat{\mathcal{L}\textit{ieb}}_\infty \] satisfying certain boundary conditions, where $\mathcal {A}\textit{ssb}_\infty$ is a minimal resolution of the prop of associative bialgebras. We prove that the set of such formality morphisms is non-empty. The latter result is used in turn to give a short proof of the formality theorem for universal quantizations of arbitrary Lie bialgebras which says that for any Drinfeld associator $\mathfrak{A}$ there is an associated ${\mathcal {L}} ie_\infty$ quasi-isomorphism between the ${\mathcal {L}} ie_\infty$ algebras $\mathsf {Def}({\mathcal {A}} ss{\mathcal {B}}_\infty \rightarrow {\mathcal {E}} nd_{\odot ^\bullet V})$ and $\mathsf {Def}({\mathcal {L}} ie{\mathcal {B}}\rightarrow {\mathcal {E}} nd_V)$ controlling, respectively, deformations of the standard bialgebra structure in $\odot V$ and deformations of any given Lie bialgebra structure in $V$. We study the deformation complex of an arbitrary universal formality morphism $\mathsf {Def}(\mathcal {A}\textit{ssb}_\infty \stackrel {F}{\rightarrow } {\mathcal {D}}\widehat {\mathcal {L}\textit{ieb}}_\infty )$ and prove that it is quasi-isomorphic to the full (i.e. not necessary connected) version of the graph complex introduced Maxim Kontsevich in the context of the theory of deformation quantizations of Poisson manifolds. This result gives a complete classification of the set $\{F_\mathfrak{A}\}$ of gauge equivalence classes of universal Lie connected formality maps: it is a torsor over the Grothendieck–Teichmüller group $GRT=GRT_1\rtimes {\mathbb {K}}^*$ and can hence can be identified with the set $\{\mathfrak{A}\}$ of Drinfeld associators.

The Weil Algebra of a Double Lie Algebroid

Given a double vector bundle $D\to M$, we define a bigraded bundle of algebras $W(D)\to M$ called the “Weil algebra bundle”. The space ${\mathcal{W}}(D)$ of sections of this algebra bundle ”realizes” the algebra of functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebra bundles of $D$ and those of the double vector bundles $D^{\prime},\ D^{\prime\prime}$ obtained from $D$ by duality operations. We show that ${\mathcal{V}\mathcal{B}}$-algebroid structures on $D$ are equivalent to horizontal or vertical differentials on two of the Weil algebras and a Gerstenhaber bracket on the 3rd. Furthermore, Mackenzie’s definition of a double Lie algebroid is equivalent to compatibilities between two such structures on any one of the three Weil algebras. In particular, we obtain a ”classical” version of Voronov’s result characterizing double Lie algebroid structures. In the case that $D=TA$ is the tangent prolongation of a Lie algebroid, we find that ${\mathcal{W}}(D)$ is the Weil algebra of the Lie algebroid, as defined by Mehta and Abad–Crainic. We show that the deformation complex of Lie algebroids, the theory of IM forms and IM multi-vector fields, and 2-term representations up to homotopy all have natural interpretations in terms of our Weil algebras.

A universal enveloping algebra for cocommutative rack bialgebras

We construct a bialgebra object in the category of linear maps {\mathcal{LM}} from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgberas, as is illustrated by a concrete example. As a separate result, we show that the Loday complex with adjoint coefficients embeds into the rack bialgebra deformation complex for the rack bialgebra defined by a Leibniz algebra.

Holonomic Poisson Manifolds and Deformations of Elliptic Algebras

This chapter introduces a natural non-degeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation spaces are as finite-dimensional as one could ever hope: the corresponding derived deformation complex is a perverse sheaf. The chapter develops some basic structural features of these manifolds, highlighting the role played by the divergence of Hamiltonian vector fields. As an application, it establishes the deformation invariance of certain families of Poisson manifolds defined by Feigin and Odesskii, along with the ‘elliptic algebras’ that quantize them.

Deformation of Dirac Structures via L∞ Algebras

The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra that depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty $ algebra instead. We develop a simplified method for describing this $L_\infty $ algebra and use it to prove that the $L_\infty $ algebras corresponding to different transversals are canonically $L_\infty $–isomorphic. In some cases, this isomorphism provides a formality map, as we show in several examples including (quasi)-Poisson geometry, Dirac structures on Lie groups, and Lie bialgebras. Finally, we apply our result to a classical problem in the deformation theory of complex manifolds; we provide explicit formulas for the Kodaira–Spencer deformation complex of a fixed small deformation of a complex manifold, in terms of the deformation complex of the original manifold.

Deformation Parameters and Fatigue of the Recycled Asphalt Mixtures

The deformational properties of asphalt mixtures measured by dynamic methods and fatigue allow a design the road to suit the expected traffic load. Quality of mixtures is also expressed by the resistance to permanent deformation. Complex modulus of stiffness and fatigue can reliably characterize the proposed mixture of asphalt pavement. The complex modulus (E*) measurement of asphalt mixtures are carried out in laboratory of Department of Construction Management at University of Žilina by two-point bending test method on trapezoid-shaped samples. Today, the fatigue is verified on trapezoid-shaped samples and is assessed by proportional strain at 1 million cycles (ε6). The test equipment and software is used to evaluate fatigue and deformation characteristics.