Development of an improved mixing model for an SRM code

Consider two gases being pumped into a container of some sort. How will they mix? How will they interact with one another? And how do you model the mixing using a computer? One way is to rst divide the two gases into smaller groups called particles and then let these particles interact with one another at random. Two of the models that is used today is CURL and Modied CURL. They work well and the results are consistent with experimental data. One drawback with them is that neither of them can handle mixing with two particles of dierent sizes. So here is presented a new model based on CURL and Modied CURL but with the extension of handling particles of dierent sizes. To test the consistency of these new models simulations are done using DARS, a product of LOGE

Vertex operators, solvable lattice models and metaplectic Whittaker functions

We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We arrive at this connection by reconsidering solvable lattice models known as `metaplectic ice' whose partition functions are metaplectic Whittaker functions. First, we show that a certain Hecke action on metaplectic Whittaker coinvariants agrees (up to twisting) with a Hecke action of Ginzburg, Reshetikhin, and Vasserot. This allows us to expand the framework of KMS by Drinfeld twisting to introduce Gauss sums into the quantum wedge, which are necessary for connections to metaplectic forms. Our main theorem interprets the row transfer matrices of this ice model as `half' vertex operators on quantum Fock space that intertwine with the action of $U_q(\widehat{\mathfrak{sl}}(n))$. In the process, we introduce new symmetric functions termed \textit{metaplectic symmetric functions} and explain how they relate to Whittaker functions on an $n$-fold metaplectic cover of GL$_r$. These resemble \textit{LLT polynomials} introduced by Lascoux, Leclerc and Thibon; in fact the metaplectic symmetric functions are (up to twisting) specializations of \textit{supersymmetric LLT polynomials} defined by Lam. Indeed Lam constructed families of symmetric functions from Heisenberg algebra actions on the Fock space commuting with the $U_q(\widehat{\mathfrak{sl}}(n))$-action. We explain that half vertex operators agree with Lam's construction and this interpretation allows for many new identities for metaplectic symmetric and Whittaker functions, including Cauchy identities. While both metaplectic symmetric functions and LLT polynomials can be related to vertex operators on the $q$-Fock space, only metaplectic symmetric functions are connected to solvable lattice models.Comment: v3 changes: minor edit

Eisenstein series and automorphic representations

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of the Langlands constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker function associated to unramified automorphic representations of G(Q_p). In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore also introduce some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In particular, we provide a detailed treatment of supersymmetry constraints on string amplitudes which enforce differential equations of the same type that are satisfied by automorphic forms. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics which go beyond the scope of this book.Comment: 326 pages. Detailed and example-driven exposition of the subject with highlighted applications to string theory. v2: 375 pages. Substantially extended and small correction

Montage

“How can we see time?” This question is raised in the opening sentence of Didi-Huberman’s book-length study of Bertolt Brecht’s 1955 photobook Kriegsfibel (War Primer in English translation (2017)), pieced together with scissors and glue from press clippings and self-penned epigrams. Three years later, in the concluding sentence of his second volume devoted to the unfinished Mnemosyne Atlas, created by the cultural historian Aby Warburg in the late 1920s, Didi-Huberman declares that the tenacious construction of montage constitutes “the difficult — and dialectical — work of anyone who attempts to see time”

Foreword

A confounding antinomy has characterized the ill-fated twenty-first century. On the one hand, a frenzy of “historical” and “unprecedented” moments, as the world is incessantly afflicted by momentous change and cataclysmic and unique events, we are told. “How historical is this?” the news anchor asks the reporter in the field or the expert in the studio, and infallibly, it’s always off the charts. On the other, a debilitating sense of inertia, of being struck by paralysis and unable to imagine alternatives to the present. The more historical moments, it seems, the less times are prone to change, and the weaker the historical agency of our species. These two phenomena coalesce in the violent resurgence of historical imaginaries of a distinctly mythical, messianic, and Manichean zeal. Thus far, the post-millennia era is bookended by the declarations of a Christian crusade to purge the world from terror, and the resurrection of the “spiritual unity” 1of Russia and the reunification of a “people bound by blood.” 2While the former was waged in the name of “the Homeland” and “American soil,” and refracted through the cultural memory of Pearl Harbor and Iwo Jima, the latter stakes its claim in the baptism of the Viking prince Valdemar, the conquests of Peter the Great, and the Great Patriotic War. In the interim, we have witnessed the campaigns to reestablish the Caliphate, draped in the archaisms of mounted knights, black banners, iconoclastic rituals, and dark punishments; to “make America great again” (that is to say, to undo the alleged post-racial era); and to “take back control” (the ironic slogan of Brexit)

Screen Violence from Settler Colonialism to Cognitive Capitalism: Westworld and the Player Piano

While the HBO show Westworld (2016–present, created by Lisa Joy and Jonathan Nolan) has gained much critical attention for its byzantine plotting and philosophical conundrums, the present discussion focuses instead on the basic premise on which the titular park operates, namely that the algorithms that govern human behavior can be disclosed by studying how human beings behave toward image beings. Under the guise of a tactile experience of a make-believe past, the park attractions clandestinely function as a large behavioral sensor, extracting actionable data from the guests who reveal their inner drives when interacting with the host environment. Taking its cue from the opening titles of the first season, the argument pivots on the master trope of the series: the machine-readable scroll of perforated paper that commands the automated performance of the player piano. This motif is examined through a double-pronged approach that aligns the anthropology of images developed by Hans Belting, which understands the relation between humans and images as the interactions between “hosts” and “guests,” with the archaeology of media and its dominant concern to uncover the prehistory of the automated control systems of the computer age. While Westworld proffers a timely allegory of biopolitical capture along the digital frontier, the show ultimately testifies to the failure to constructively engage with the precarious relation between hosts and guests that to an equal extent defines our contemporary moment. The initial problem raised by Westworld, the ethics of killing virtual beings, thus gives rise to a broader historical inquiry that concerns the inability of human societies to face the past and deal with the images they inherit

In Spite of All (Malgré tout)

The locution malgré tout, ‘in spite of all’ or ‘despite everything’, is first and foremost associated with the vexed debate stirred by the exhibition Mémoire des camps, which was organized in Paris in 2001, and the violent reactions provoked by Didi-Huberman’s catalogue essay, “l’images malgré tout”, subsequently expanded into the eponymously titled book in response to the fierce criticisms. Didi-Huberman’s conception of the four photographs taken by a member of the Sonderkommando, the ‘special units’ of Jewish prisoners whose task it was to dispose of the corpses at Birkenau in August 1944, as acts of resistance, as visual testimonies, and as “survivors” (ISA, p.46), was first attacked by Claude Lanzmann, in an interview in Le Monde (2001), and soon followed by Gérard Wajcman in Les temps modernes (2001; see also Pagnoux, 2001). In his article, Wajcman accused Didi-Huberman not only of corroborating the logic of Holocaust deniers, who demand that the event is yet to be proved, but, primarily, of Christianizing the Shoah by means of images

Soft nanostructuring of YBCO Josephson Junctions by phase separation

We have developed a new method to fabricate biepitaxial YBa2Cu3O(7-x) (YBCO) Josephson junctions at the nanoscale, allowing junctions widths down to 100 nm and simultaneously avoiding the typical damage in grain boundary interfaces due to conventional patterning procedures. By using the competition between the superconducting YBCO and the insulating Y2BaCuO5 phases during film growth, we formed nanometer sized grain boundary junctions in the insulating Y2BaCuO5 matrix as confirmed by high resolution transmission electron microscopy. Electrical transport measurements give clear indications that we are close to probing the intrinsic properties of the grain boundaries.Comment: 16 pages, 6 figure

A reduction principle for Fourier coefficients of automorphic forms

In this paper we analyze a general class of Fourier coefficients of automorphic forms on reductive adelic groups $\mathbf{G}(\mathbb{A}_\mathbb{K})$ and their covers. We prove that any such Fourier coefficient is expressible through integrals and sums involving 'Levi-distinguished' Fourier coefficients. By the latter we mean the class of Fourier coefficients obtained by first taking the constant term along the nilradical of a parabolic subgroup, and then further taking a Fourier coefficient corresponding to a $\mathbb{K}$-distinguished nilpotent orbit in the Levi quotient. In a follow-up paper we use this result to establish explicit formulas for Fourier expansions of automorphic forms attached to minimal and next-to-minimal representations of simply-laced reductive groups.Comment: 35 pages. v2: Extended results and paper split into two parts with second part appearing soon. New title to reflect new focus of this part. v3: Minor corrections and updated reference to the second part that has appeared as arXiv:1908.08296. v4: Minor corrections and reformulation