Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some previous results of Lawrence and Rozansky, the Chern-Simons partition function with arbitrary simply-laced group for these spaces is written in terms of matrix integrals. The analysis of the perturbative expansion amounts to the evaluation of averages in a Gaussian ensemble of random matrices. As a result, explicit expressions for the universal perturbative invariants of Seifert homology spheres up to order five are presented.Comment: 26 pages, JHEP style, typos corrected, some improvements in section 5.2, references adde

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

Self-intersection local times of random walks: Exponential moments in subcritical dimensions

Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$. We derive precise logarithmic asymptotics of the expectation of $\exp\{\theta_t \|\ell_t\|_p\}$ for scales $\theta_t>0$ that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of $t$ and $\theta_t$, and the precise rate is characterized in terms of a variational formula, which is in close connection to the {\it Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation principle for $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk homogeneously squeezes in a $t$-dependent box with diameter of order $\ll t^{1/d}$ to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The final publication is available at springerlink.co

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

A straightforward expansion of Edwards' functional integral representation of the grand partition function for a polymer liquid as an infinite set of Feynman diagrams is shown to yield a cluster expansion that is closely related to the corresponding Mayer cluster expansion developed for flexible molecules by Chandler and coworkers. The procedure initially yields a perturbative cluster expansion in which all free energies and correlation functions are expressed diagrammatically as functionals of single-molecule correlation functions of non-interacting molecules. Topological reduction yields several renormalized expansions for collective correlation functions of all orders as functionals of single-molecule correlation functions in the interacting fluid. Renormalized expansions are also obtained for a generalized Ornstein-Zernicke (OZ) direct correlation function and for intramolecular correlation functions. The application of the formalism to coarse-grained models of polymer fluids is discussed, and a loop expansion about self-consistent field theory is shown to converge for sufficiently coarse-grained models, in which monomers are strongly overlapping. The formalism is used to derive a new expression for the OZ direct correlation function and to recover known results for the 2-point intramolecular correlation function to first order in a loop expansion, for binary blends and diblock copolymer melts.Comment: 98 pages, 13 figures, accepted by Annals of Physic

Critical Indices as Limits of Control Functions

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the role of control functions governing the fastest convergence of the renormalized series. A striking relation between the theory of critical phenomena and optimal control theory is discovered: The critical indices are found to be directly related to limits of control functions at critical points. The method is applied to calculating the critical indices for several difficult problems. The results are in very good agreement with accurate numerical data.Comment: 1 file, 5 pages, RevTe

The Wnt5a Receptor, Receptor Tyrosine Kinase-Like Orphan Receptor 2, Is a Predictive Cell Surface Marker of Human Mesenchymal Stem Cells with an Enhanced Capacity for Chondrogenic Differentiation

Multipotent mesenchymal stem cells (MSCs) have enormous potential in tissue engineering and regenerative medicine. However until now their development for clinical use has been severely limited as they are a mixed population of cells with varying capacities for lineage differentiation and tissue formation. Here we identify ROR2 as a cell surface marker expressed by those MSCs with an enhanced capacity for cartilage formation. We generated clonal human MSC populations with varying capacities for chondrogenesis. ROR2 was identified through screening for upregulated genes in the most chondrogenic clones. When isolated from un-cloned populations, ROR2+ve MSCs were significantly more chondrogenic than either ROR2-ve or unfractionated MSCs. In a sheep cartilage-repair model they produced significantly more defect filling with no loss of cartilage quality compared with controls. ROR2+ve MSCs/perivascular cells were present in developing human cartilage, adult bone marrow and adipose tissue. Their frequency in bone marrow was significantly lower in patients with osteoarthritis than in controls. However after isolation of these cells and their initial expansion in vitro, there was greater ROR2 expression in the population derived from osteoarthritis patients compared with controls. Furthermore, osteoarthritis-derived MSCs were better able to form cartilage than MSCs from control patients in a tissue engineering assay. We conclude that MSCs expressing high levels of ROR2 provide a defined population capable of predictably enhanced cartilage production. This article is protected by copyright. All rights reserved

Directed Polymers with Random Interaction : An Exactly Solvable Case -

We propose a model for two $(d+1)$-dimensional directed polymers subjected to a mutual $\delta$-function interaction with a random coupling constant, and present an exact renormalization group study for this system. The exact $\beta$-function, evaluated through an $\epsilon(=1-d)$ expansion for second and third moments of the partition function, exhibits the marginal relevance of the disorder at $d=1$, and the presence of a phase transition from a weak to strong disorder regime for $d>1$. The lengthscale exponent for the critical point is $\nu=1/2\mid\epsilon\mid$. We give details of the renormalization. We show that higher moments do not require any new interaction, and hence the $\beta$ function remains the same for all moments. The method is extended to multicritical systems involving an $m$ chain interaction. The corresponding disorder induced phase transition for $d>d_m=1/(m-1)$ has the critical exponent ${\nu}_m=[2d(m-1)-2]^{-1}$. For both the cases, an essential singularity appears for the lengthscale right at the upper critical dimension $d_m$. We also discuss the strange behavior of an annealed system with more than two chains with pairwise random interactions among each other.Comment: No of pages: 36, 7figures on request, Revtex3, Report No:IP/BBSR/929

Southern San Andreas-San Jacinto fault system slip rates estimated from earthquake cycle models constrained by GPS and interferometric synthetic aperture radar observations

We use ground geodetic and interferometric synthetic aperture radar satellite observations across the southern San Andreas (SAF)-San Jacinto (SJF) fault systems to constrain their slip rates and the viscosity structure of the lower crust and upper mantle on the basis of periodic earthquake cycle, Maxwell viscoelastic, finite element models. Key questions for this system are the SAF and SJF slip rates, the slip partitioning between the two main branches of the SJF, and the dip of the SAF. The best-fitting models generally have a high-viscosity lower crust (η = 10^(21) Pa s) overlying a lower-viscosity upper mantle (η = 10^(19) Pa s). We find considerable trade-offs between the relative time into the current earthquake cycle of the San Jacinto fault and the upper mantle viscosity. With reasonable assumptions for the relative time in the earthquake cycle, the partition of slip is fairly robust at around 24–26 mm/a for the San Jacinto fault system and 16–18 mm/a for the San Andreas fault. Models for two subprofiles across the SAF-SJF systems suggest that slip may transfer from the western (Coyote Creek) branch to the eastern (Clark-Superstition hills) branch of the SJF from NW to SE. Across the entire system our best-fitting model gives slip rates of 2 ± 3, 12 ± 9, 12 ± 9, and 17 ± 3 mm/a for the Elsinore, Coyote Creek, Clark, and San Andreas faults, respectively, where the large uncertainties in the slip rates for the SJF branches reflect the large uncertainty in the slip rate partitioning within the SJF system

Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter

We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kaehler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kaehler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative alpha'-corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP_6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP_3 singularity.Comment: 49 pages, 5 figures; v2: references adde

Active megadetachment beneath the western United States

Geodetic data, interpreted in light of seismic imaging, seismicity, xenolith studies, and the late Quaternary geologic history of the northern Great Basin, suggest that a subcontinental-scale extensional detachment is localized near the Moho. To first order, seismic yielding in the upper crust at any given latitude in this region occurs via an M7 earthquake every 100 years. Here we develop the hypothesis that since 1996, the region has undergone a cycle of strain accumulation and release similar to “slow slip events” observed on subduction megathrusts, but yielding occurred on a subhorizontal surface 5–10 times larger in the slip direction, and at temperatures >800°C. Net slip was variable, ranging from 5 to 10 mm over most of the region. Strain energy with moment magnitude equivalent to an M7 earthquake was released along this “megadetachment,” primarily between 2000.0 and 2005.5. Slip initiated in late 1998 to mid-1999 in northeastern Nevada and is best expressed in late 2003 during a magma injection event at Moho depth beneath the Sierra Nevada, accompanied by more rapid eastward relative displacement across the entire region. The event ended in the east at 2004.0 and in the remainder of the network at about 2005.5. Strain energy thus appears to have been transmitted from the Cordilleran interior toward the plate boundary, from high gravitational potential to low, via yielding on the megadetachment. The size and kinematic function of the proposed structure, in light of various proxies for lithospheric thickness, imply that the subcrustal lithosphere beneath Nevada is a strong, thin plate, even though it resides in a high heat flow tectonic regime. A strong lowermost crust and upper mantle is consistent with patterns of postseismic relaxation in the southern Great Basin, deformation microstructures and low water content in dunite xenoliths in young lavas in central Nevada, and high-temperature microstructures in analog surface exposures of deformed lower crust. Large-scale decoupling between crust and upper mantle is consistent with the broad distribution of strain in the upper crust versus the more localized distribution in the subcrustal lithosphere, as inferred by such proxies as low P wave velocity and mafic magmatism