25,124 research outputs found
Multiple Heat Exchangers Simulation Within the Newton-Raphson Framework
A general framework is proposed for simulating complex heat exchanger geometries in a manner suitable
for sequential solution of the refrigerant- and air-side equations for mass, momentum and energy. The sequential
solution enables the algorithm to be applied to a single module of a complex heat exchanger, and then integrated
with other modules within a simultaneous equation solver employing a Newton-Raphson approach. This report also
describes the integration of component subroutines into system simulation models for air conditioners and
refrigerators. The modular approach is illustrated by describing its application to a dual-evaporator refrigerator
simulation.Air Conditioning and Refrigeration Project 6
Blowup Equations for Refined Topological Strings
G\"{o}ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the
Nekrasov partition function of five dimensional supersymmetric
gauge theories compactified on a circle, which via geometric engineering
correspond to the refined topological string theory on geometries. In
this paper, we study the K-theoretic blowup equations for general local
Calabi-Yau threefolds. We find that both vanishing and unity blowup equations
exist for the partition function of refined topological string, and the crucial
ingredients are the fields introduced in our previous paper. These
blowup equations are in fact the functional equations for the partition
function and each of them results in infinite identities among the refined free
energies. Evidences show that they can be used to determine the full refined
BPS invariants of local Calabi-Yau threefolds. This serves an independent and
sometimes more powerful way to compute the partition function other than the
refined topological vertex in the A-model and the refined holomorphic anomaly
equations in the B-model. We study the modular properties of the blowup
equations and provide a procedure to determine all the vanishing and unity fields from the polynomial part of refined topological string at large
radius point. We also find that certain form of blowup equations exist at
generic loci of the moduli space.Comment: 85 pages. v2: Journal versio
Numerical calculation of three-point branched covers of the projective line
We exhibit a numerical method to compute three-point branched covers of the
complex projective line. We develop algorithms for working explicitly with
Fuchsian triangle groups and their finite index subgroups, and we use these
algorithms to compute power series expansions of modular forms on these groups.Comment: 58 pages, 24 figures; referee's comments incorporate
On computing Belyi maps
We survey methods to compute three-point branched covers of the projective
line, also known as Belyi maps. These methods include a direct approach,
involving the solution of a system of polynomial equations, as well as complex
analytic methods, modular forms methods, and p-adic methods. Along the way, we
pose several questions and provide numerous examples.Comment: 57 pages, 3 figures, extensive bibliography; English and French
abstract; revised according to referee's suggestion
The Omega deformed B-model for rigid N=2 theories
We give an interpretation of the Omega deformed B-model that leads naturally
to the generalized holomorphic anomaly equations. Direct integration of the
latter calculates topological amplitudes of four dimensional rigid N=2 theories
explicitly in general Omega-backgrounds in terms of modular forms. These
amplitudes encode the refined BPS spectrum as well as new gravitational
couplings in the effective action of N=2 supersymmetric theories. The rigid N=2
field theories we focus on are the conformal rank one N=2 Seiberg-Witten
theories. The failure of holomorphicity is milder in the conformal cases, but
fixing the holomorphic ambiguity is only possible upon mass deformation. Our
formalism applies irrespectively of whether a Lagrangian formulation exists. In
the class of rigid N=2 theories arising from compactifications on local
Calabi-Yau manifolds, we consider the theory of local P2. We calculate motivic
Donaldson-Thomas invariants for this geometry and make predictions for
generalized Gromov-Witten invariants at the orbifold point.Comment: 73 pages, no figures, references added and typos correcte
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