Gradient flow approach to an exponential thin film equation: global existence and latent singularity

In this work, we study a fourth order exponential equation, $u_t=\Delta e^{-\Delta u},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.Comment: latent singularity, curve of maximal slope. arXiv admin note: text overlap with arXiv:1711.07405 by other author

Collapse simulation of a typical super-tall RC frame-core tube building exposed to extreme fire

The previous fire accidents proofed that reinforced concrete (RC) structures may experience progressive collapse subjected to extreme fires. In consequence, the study on the extreme fire-induced progressive collapse of RC structures is important for the safety of buildings. However, limited study has been performed on the extreme fire-induced progressive collapse of super-tall buildings. In this work, a finite element (FE) model and the corresponding elemental deactivation technology is proposed to simulate the extreme fire-induced progressive collapse of a typical super-tall RC frame-core tube building. The simulation discovered that the collapse of the building is initiated by the flexural failure of perimeter columns because of the thermal expansion of the floor system. The mechanism that discovered can provide a reference for related research of the fire safety of RC buildings

Non-SUSY pp-branes delocalized in two directions, tachyon condensation and T-duality

We here generalize our previous construction [hep-th/0409019] of non-supersymmetric $p$-branes delocalized in one transverse spatial direction to two transverse spatial directions in supergravities in arbitrary dimensions ($d$). These solutions are characterized by five parameters. We show how these solutions in $d=10$ interpolate between D($p+2$)-anti-D($p+2$) brane system, non-BPS D$(p+1)$-branes (delocalized in one direction) and BPS D$p$-branes by adjusting and scaling the parameters in suitable ways. This picture is very similar to the descent relations obtained by Sen in the open string effective description of non-BPS D$(p+1)$ brane and BPS D$p$-brane as the respective tachyonic kink and vortex solutions on the D$(p+2)$-anti-D$(p+2)$ brane system (with some differences). We compare this process with the T-duality transformation which also has the effect of increasing (or decreasing) the dimensionality of the branes by one.Comment: 19 pages, late

Steady state analytical solutions for pumping in a fully bounded rectangular aquifer

Using the Schwartz-Christoffel conformal mapping method together with the complex variable techniques, we derive steady state analytical solutions for pumping in a rectangular aquifer with four different combinations of impermeable and constant-head boundaries. These four scenarios include: (1) one constant-head boundary and three impermeable boundaries, (2) two pairs of orthogonal impermeable and constant-head boundaries, (3) three constant-head boundaries and one impermeable boundary, and (4) four constant-head boundaries. For these scenarios, the impermeable and constant-head boundaries can be combined after applying the mapping functions, and hence only three image wells exist in the transformed plane, despite an infinite number of image wells in the real plane. The closed-form solutions reflect the advantage of the conformal mapping method, though the method is applicable for the aspect ratio of the rectangle between 1/10.9 and 10.9/1 due to the limitation in the numerical computation of the conformal transformation from a half plane onto an elongated region (i.e., so-called “crowding” phenomenon). By contrast, for an additional scenario with two parallel constant-head boundaries and two parallel impermeable boundaries, an infinite series of image wells is necessary to express the solution, since it is impossible to combine these two kinds of boundaries through the conformal transformation. The usefulness of the results derived is demonstrated by an application to pumping in a finite coastal aquifer

Analytical solutions of seawater intrusion in sloping confined and unconfined coastal aquifers

Sloping coastal aquifers in reality are ubiquitous and well documented. Steady state sharp-interface analytical solutions for describing seawater intrusion in sloping confined and unconfined coastal aquifers are developed based on the Dupuit-Forchheimer approximation. Specifically, analytical solutions based on the constant-flux inland boundary condition are derived by solving the discharge equation for the interface zone with the continuity conditions of the head and flux applied at the interface between the freshwater zone and the interface zone. Analytical solutions for the constant-head inland boundary are then obtained by developing the relationship between the inland freshwater flux and hydraulic head and combining this relationship with the solutions of the constant-flux inland boundary. It is found that for the constant-flux inland boundary, the shape of the saltwater interface is independent of the geometry of the bottom confining layer for both aquifer types, despite that the geometry of the bottom confining layer determines the location of the interface tip. This is attributed to that the hydraulic head at the interface is identical to that of the coastal boundary, so the shape of the bed below the interface is irrelevant to the interface position. Moreover, developed analytical solutions with an empirical factor on the density factor are in good agreement with the results of variable-density flow numerical modeling. Analytical solutions developed in this study provide a powerful tool for assessment of seawater intrusion in sloping coastal aquifers as well as in coastal aquifers with a known freshwater flux but an arbitrary geometry of the bottom confining layer