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We introduce a new class of nonlocal nonlinear conservation laws in one space dimension that allow for nonlocal interactions over a finite horizon. The proposed model, which we refer to as the nonlocal pair interaction model, inherits at the continuum level the unwinding feature of finite difference schemes for local hyperbolic conservation laws, so that the maximum principle and certain monotonicity properties hold and, consequently, the entropy inequalities are naturally satisfied. We establish a global-in-time well-posedness theory for these models which covers a broad class of initial data. Moreover, in the limit when the horizon parameter approaches zero, we are able to prove that our nonlocal model reduces to the conventional class of local hyperbolic conservation laws. Furthermore, we propose a numerical discretization method adapted to our nonlocal model, which relies on a monotone numerical flux and a uniform mesh, and we establish that these numerical solutions converge to a solution, providing as by-product both the existence theory for the nonlocal model and the convergence property relating the nonlocal regime and the asymptotic local regime.where the given numerical flux g is a Lipschitz continuous function consistent with the flux f = f (u), in the sense that g(u, u) = f (u). It is well known that if g = g(u, v) is a monotone flux, i.e, is non-decreasing in u and non-increasing in v, then the scheme (1.2) is Total Variation Diminishing (TVD) and enjoys the Maximum Principle [11,32]. By picking appropriate choice of g satisfying the

Effect of microcapsules on cement composites has been studied. The hydration of cement composite using microcapsules is studied by XRD and thermal techniques, showing that the addition of microcapsules has little affect on the hydration of cement. The pore size distribution and surface area of the cement composite with microcapsule are analyzed, showing a reduction in the pore content of cement composite and makes the pores smaller, which would improve durability and impermeability for designed materials. Damaging on cement and composites containing microcapsules and self-healing of these damagings can be reflected by the changes in their bending strength. When the cracks were generated in the composite, the microcapsules can release adhesive to fill in the space between the crackings, preventing cracking further growth.

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