751 research outputs found
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 -fold cover of the
general linear group arise naturally from the quantum Fock space representation
of 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
.
In the process, we introduce new symmetric functions termed
\textit{metaplectic symmetric functions} and explain how they relate to
Whittaker functions on an -fold metaplectic cover of GL. 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 -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 -Fock space, only metaplectic symmetric functions are connected to
solvable lattice models.Comment: v3 changes: minor edit
Montage
âHow can we see time?â This question is raised in the opening sentence of Didi-Hubermanâs book-length study of Bertolt Brechtâs 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 âthe difficult â and dialectical â work of anyone who attempts to see timeâ
Foreword
A confounding antinomy has characterized the ill-fated twenty-first century. On the one hand, a frenzy of âhistoricalâ and âunprecedentedâ moments, as the world is incessantly afflicted by momentous change and cataclysmic and unique events, we are told. âHow historical is this?â the news anchor asks the reporter in the field or the expert in the studio, and infallibly, itâs 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 âspiritual unityâ 1of Russia and the reunification of a âpeople bound by blood.â 2While the former was waged in the name of âthe Homelandâ and âAmerican soil,â 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 âmake America great againâ (that is to say, to undo the alleged post-racial era); and to âtake back controlâ (the ironic slogan of Brexit)
Screen Violence from Settler Colonialism to Cognitive Capitalism: Westworld and the Player Piano
While the HBO show Westworld (2016âpresent, 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 âhostsâ and âguests,â 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
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
In Spite of All (Malgré tout)
The locution malgrĂ© tout, âin spite of allâ or âdespite everythingâ, is first and foremost associated with the vexed debate stirred by the exhibition MĂ©moire des camps, which was organized in Paris in 2001, and the violent reactions provoked by Didi-Hubermanâs catalogue essay, âlâimages malgrĂ© toutâ, subsequently expanded into the eponymously titled book in response to the fierce criticisms. Didi-Hubermanâs conception of the four photographs taken by a member of the Sonderkommando, the âspecial unitsâ 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 âsurvivorsâ (ISA, p.46), was first attacked by Claude Lanzmann, in an interview in Le Monde (2001), and soon followed by GĂ©rard 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
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 -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
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