The structure of supersonic underexpanded nitrogen microjets

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.This article contains the results of investigating the gas-dynamic structure of supersonic underexpanded axisymmetric microjets of nitrogen flowing from sound nozzles with a diameter of 10 ÷ 340 μm. The length of the supersonic part of the jet significantly increases together with a decrease in nozzle diameter starting from the size 23 μm. Measurement results are compared with known data obtained for macro- and microjets

Alternative splicing and protein function

BACKGROUND: Alternative splicing is a major mechanism of generating protein diversity in higher eukaryotes. Although at least half, and probably more, of mammalian genes are alternatively spliced, it was not clear, whether the frequency of alternative splicing is the same in different functional categories. The problem is obscured by uneven coverage of genes by ESTs and a large number of artifacts in the EST data. RESULTS: We have developed a method that generates possible mRNA isoforms for human genes contained in the EDAS database, taking into account the effects of nonsense-mediated decay and translation initiation rules, and a procedure for offsetting the effects of uneven EST coverage. Then we computed the number of mRNA isoforms for genes from different functional categories. Genes encoding ribosomal proteins and genes in the category "Small GTPase-mediated signal transduction" tend to have fewer isoforms than the average, whereas the genes in the category "DNA replication and chromosome cycle" have more isoforms than the average. Genes encoding proteins involved in protein-protein interactions tend to be alternatively spliced more often than genes encoding non-interacting proteins, although there is no significant difference in the number of isoforms of alternatively spliced genes. CONCLUSION: Filtering for functional isoforms satisfying biological constraints and accountung for uneven EST coverage allowed us to describe differences in alternative splicing of genes from different functional categories. The observations seem to be consistent with expectations based on current biological knowledge: less isoforms for ribosomal and signal transduction proteins, and more alternative splicing of interacting and cell cycle proteins

Gauge Theory Wilson Loops and Conformal Toda Field Theory

The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.Comment: 17 pages, 3 figures; references added

On AGT description of N=2 SCFT with N_f=4

We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N_f=4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.Comment: 18 pages. v2, a misinterpretation in the gauge theory side has been corrected; title and introduction were changed accordingl

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories

Recently Alday and Tachikawa proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N) symmetry and instanton partition functions in conformal N=2 SU(N) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N=2 SU(N) theories.Comment: 40 pages. v2: minor changes and clarification

Classical conformal blocks from TBA for the elliptic Calogero-Moser system

The so-called Poghossian identities connecting the toric and spherical blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain expressions for the classical 4-point block on the sphere. The main motivation for this line of research is the longstanding open problem of uniformization of the 4-punctured Riemann sphere, where the 4-point classical block plays a crucial role. It is found that the obtained representation for certain 4-point classical blocks implies the relation between the accessory parameter of the Fuchsian uniformization of the 4-punctured sphere and the eCMY functional. Additionally, a relation between the 4-point classical block and the $N_f=4$, ${\sf SU(2)}$ twisted superpotential is found and further used to re-derive the instanton sector of the Seiberg-Witten prepotential of the $N_f=4$, ${\sf SU(2)}$ supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio

The matrix model version of AGT conjecture and CIV-DV prepotential

Recently exact formulas were provided for partition function of conformal (multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q_a-expansion, where q_a parameterize the shape of the Penner potential, and are exact in the filling numbers N_a. At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary beta and to non-polynomial potentials, provides an alternative expansion: in powers of N_a and exact in q_a. We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q_a and N_a. This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.Comment: 27 pages, 1 figur

Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions

We give a concise summary of the impressive recent development unifying a number of different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric series) form a full basis for all conformal blocks of the Virasoro algebra and are sufficient to provide the same for some (special) conformal blocks of W-algebras. They can be described in terms of Seiberg-Witten theory, with the SW differential given by the 1-point resolvent in the DV phase of the quiver (discrete or conformal) matrix model (\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p} \rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNS parameters \epsilon_1 and \epsilon_2. This provides explicit formulas for conformal blocks in terms of analytically continued contour integrals and resolves the old puzzle of the free-field description of generic conformal blocks through the Dotsenko-Fateev integrals. Most important, this completes the GKMMM description of SW theory in terms of integrability theory with the help of exact BS integrals, and provides an extended manifestation of the basic principle which states that the effective actions are the tau-functions of integrable hierarchies.Comment: 14 page

Non-Perturbative Topological Strings And Conformal Blocks

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.Comment: 36 page

Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants

Inspired by the work of Alday, Gaiotto and Tachikawa (AGT), we saw the revival of Poincar{\'{e}}'s uniformization problem and Fuchsian equations obtained thereof. Three distinguished aspects are possessed by Fuchsian equations. First, they are available via imposing a classical Liouville limit on level-two null-vector conditions. Second, they fall into some A_1-type integrable systems. Third, the stress-tensor present there (in terms of the Q-form) manifests itself as a kind of one-dimensional "curve". Thereby, a contact with the recently proposed Nekrasov-Shatashvili limit was soon made on the one hand, whilst the seemingly mysterious derivation of Seiberg-Witten prepotentials from integrable models become resolved on the other hand. Moreover, AGT conjecture can just be regarded as a quantum version of the previous Poincar{\'{e}}'s approach. Equipped with these observations, we examined relations between spheric and toric (classical) conformal blocks via Calogero-Moser/Heun duality. Besides, as Sutherland model is also obtainable from Calogero-Moser by pinching tori at one point, we tried to understand its eigenstates from the viewpoint of toric diagrams with possibly many surface operators (toric branes) inserted. A picture called "bubbling pants" then emerged and reproduced well-known results of the non-critical self-dual c=1 string theory under a "blown-down" limit.Comment: 17 pages, 4 figures; v2: corrections and references added; v3: Section 2.4.1 newly added thanks to JHEP referee advice. That classical four-point spheric conformal blocks reproducing known SW prepotentials is demonstrated via more examples, to appear in JHEP; v4: TexStyle changed onl