On a differential inclusion related to the Born-Infeld equations

We study a partial differential relation that arises in the context of the Born-Infeld equations (an extension of the Maxwell's equations) by using Gromov's method of convex integration in the setting of divergence free fields

New selective dissolution process to quantify reaction extent and product stability in metakaolin-based geopolymers

A selective dissolution process is developed that can quantify the amount of soluble material, geopolymer gel and remnant unreacted precursor in metakaolin-based geopolymer systems and determine the nanostructural features of the raw materials and geopolymer gel components. The susceptibility of alkalis leachability from the alkaline aluminosilicate hydrate-type gel (N-A-S-H) produced during the geopolymerization is not fully understood. This phenomenon led to deleterious processes from a microstructural, aesthetic and performance point of view. Geopolymers were synthesised using different contents and types of alkalis (M/Al = 0.50–0.83, where M represents Na or K), different contents of soluble silica in the activator (expressed as SiO2/M2O ratio of 1.0, 0.5 and 0.0), and curing temperatures (25 and 50 °C). The selective dissolution process is based on neutral dissolution at pH 7 to extract the soluble materials and acid dissolution using a strong acid at pH 0 to dissolve the geopolymer gel, which provides for the first time a method to quantify the (i) soluble material, (ii) geopolymer gel and (iii) unreacted material in geopolymers. The soluble material provides a reliable indication of the materials that can be removed from the geopolymers in a neutral pH environment and hence the potential for leaching and efflorescence, which is useful for durability prediction and service life. Quantification of remnant unreacted metakaolin determines the reactivity of the precursor and assesses the suitability of different synthesis conditions for varied applications. This work therefore provides a novel and widely applicable approach to determine the susceptibility of geopolymer materials to leaching

Metakaolin-based geopolymers: Relation between formulation, physicochemical properties and efflorescence formation

The efflorescence formation in metakaolin-based geopolymers is assessed in this study to provide a better understanding of the effect of the synthesis parameters. Efflorescence formation depends on the physical and chemical properties of geopolymers as well as the environmental exposure conditions. In this study a set of fifteen geopolymers were synthesized using different formulation. An accelerated test of efflorescence development is presented, where the grade of degradation was evaluated by visual observation and correlated to leaching potential, physical properties and microstructural features. The use of soluble silicate in the activator provides a denser and a less permeable matrix. This makes the extraction of free alkalis to the surface more difficult, reducing the extent of alkali leaching and therefore efflorescence. The use of K+ is also effective to reduce visible efflorescence. The efflorescence formation is predicted by the properties of the gel formed which are dependent on the mix proportioning

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Properties of additive-manufactured open porous titanium structures for patient-specific load-bearing implants

Additive manufacturing has been well established in many sectors, including the medical industry. For load-bearing bone implants, titanium and its alloys, such as Ti6Al4V, are widely used due to their high strength to weight ratio and osseointegrative properties. However, bone resorption and loosening of implants is related to the significantly higher stiffness of dense Ti6Al4V, leading to stress shielding. With the aging of population, there is an increasing need for orthopedic implants with a high success rate and a long implant life span. Besides that the treatment of non-healing segmental bone defects, where the self repairing properties of bone tissue are not sufficient, is still a challenge. In both fields of application, patient-specific titanium implants combined with functionally graded porosity designed according to locally expected loads unlock new possibilities. Many studies underline the huge potential of the new design freedom to generate open porous structures and more personalized implants with enhanced mechanical properties that also integrate well with surrounding tissues. Integration of functionally graded open porosity into implants allows for the implant to more closely mimic the mechanical properties of human bone and its internal architecture. The results of this work represent the basis for developing complex porous titanium structures with various pore sizes and shapes to tailor structural mechanical properties and biological responses. Therefore, 3D porous structures with various pore sizes and shapes were designed and manufactured in Ti6Al4V using laser powder bed fusion (PBF-LB/M). Based on these structures, the correlation of pore size and shape with cell ingrowth, morphology, metabolic activity, and early markers for bone formation (ALP activity) was investigated in static cell cultures using the osteosarcoma cell line Saos-2. Mechanical properties, such as stiffness and compression strength, were investigated with compression testing. The present study concludes that cell morphology, metabolic activity, and ALP activity are widely independent of pore shape and size within the tested range of 400–700 µm pore size. Furthermore, the mechanical properties of the evaluated structures were in the range of cortical and trabecular bone. This opens the possibility to design mechanical properties with gradient porosity without decisively affecting biological responses

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs

Entangled Stories: The Red Jews in Premodern Yiddish and German Apocalyptic Lore

“Far, far away from our areas, somewhere beyond the Mountains of Darkness, on the other side of the Sambatyon River…there lives a nation known as the Red Jews.” The Red Jews are best known from classic Yiddish writing, most notably from Mendele's Kitser masoes Binyomin hashlishi (The Brief Travels of Benjamin the Third). This novel, first published in 1878, represents the initial appearance of the Red Jews in modern Yiddish literature. This comical travelogue describes the adventures of Benjamin, who sets off in search of the legendary Red Jews. But who are these Red Jews or, in Yiddish, di royte yidelekh? The term denotes the Ten Lost Tribes of Israel, the ten tribes that in biblical times had composed the Northern Kingdom of Israel until they were exiled by the Assyrians in the eighth century BCE. Over time, the myth of their return emerged, and they were said to live in an uncharted location beyond the mysterious Sambatyon River, where they would remain until the Messiah's arrival at the end of time, when they would rejoin the rest of the Jewish people. This article is part of a broader study of the Red Jews in Jewish popular culture from the Middle Ages through modernity. It is partially based on a chapter from my book, Umstrittene Erlöser: Politik, Ideologie und jüdisch-christlicher Messianismus in Deutschland, 1500–1600 (Göttingen: Vandenhoeck & Ruprecht, 2011). Several postdoctoral fellowships have generously supported my research on the Red Jews: a Dr. Meyer-Struckmann-Fellowship of the German Academic Foundation, a Harry Starr Fellowship in Judaica/Alan M. Stroock Fellowship for Advanced Research in Judaica at Harvard University, a research fellowship from the Heinrich Hertz-Foundation, and a YIVO Dina Abramowicz Emerging Scholar Fellowship. I thank the organizers of and participants in the colloquia and conferences where I have presented this material in various forms as well as the editors and anonymous reviewers of AJS Review for their valuable comments and suggestions. I am especially grateful to Jeremy Dauber and Elisheva Carlebach of the Institute for Israel and Jewish Studies at Columbia University, where I was a Visiting Scholar in the fall of 2009, for their generous encouragement to write this article. Sue Oren considerably improved my English. The style employed for Romanization of Yiddish follows YIVO's transliteration standards. Unless otherwise noted, translations from the Yiddish, Hebrew, German, and Latin are my own. Quotations from the Bible follow the JPS translation, and those from the Babylonian Talmud are according to the Hebrew-English edition of the Soncino Talmud by Isidore Epstein

Methamphetamine induces Shati/Nat8L expression in the mouse nucleus accumbens via CREB- and dopamine D1 receptor-dependent mechanism

Shati/Nat8L significantly increased in the nucleus accumbens (NAc) of mice after repeated methamphetamine (METH) treatment. We reported that Shati/Nat8L overexpression in mouse NAc attenuated METH-induced hyperlocomotion, locomotor sensitization, and conditioned place preference. We recently found that Shati/Nat8L overexpression in NAc regulates the dopaminergic neuronal system via the activation of group II mGluRs by elevated Nacetylaspartylglutamate following N-acetylaspartate increase due to the overexpression. These findings suggest that Shati/Nat8L suppresses METH-induced responses. However, the mechanism by which METH increases the Shati/Nat8L mRNA expression in NAc is unclear. To investigate the regulatory mechanism of Shati/Nat8L mRNA expression, we performed a mouse Shati/Nat8L luciferase assay using PC12 cells. Next, we investigated the response of METH to Shati/Nat8L expression and CREB activity using mouse brain slices of NAc, METH administration to mice, and western blotting for CREB activity of specific dopamine receptor signals in vivo and ex vivo. We found that METH activates CREB binding to the Shati/Nat8L promoter to induce the Shati/Nat8L mRNA expression. Furthermore, the dopamine D1 receptor antagonist SCH23390, but not the dopamine D2 receptor antagonist sulpiride, inhibited the upregulation of Shati/Nat8L and CREB activities in the mouse NAc slices. Thus, the administration of the dopamine D1 receptor agonist SKF38393 increased the Shati/Nat8L mRNA expression in mouse NAc. These results showed that the Shati/ Nat8L mRNA was increased by METH-induced CREB pathway via dopamine D1 receptor signaling in mouse NAc. These findings may contribute to development of a clinical tool for METH addiction