Fractal injectors to intensify liquid-phase processes by controlling the turbulent flow field

Fractal injectors can be used to intensify liquid-phase processes. The flow field, vortex structure and turbulent mixing performance induced by fractal injectors with three different fractal dimensions (D = 2, 2.58 and 3) are investigated. CFD simulations, using a renormalization group (RNG) k-ε turbulence model, are validated with particle image velocimetry (PIV) measurements. The structure and formation mechanism of the vortices are studied. Both spiral and double toroidal vortices are produced, the latter by jet impingement. These vortices interact with each other within a fractal generating unit. For the same total volumetric flow rate, a fractal injector with D = 2.58 can achieve better mixing uniformity than fractal injectors with D = 2 or D = 3, while maintaining a similarly high mixing rate to when D = 2. This is due to enhanced entrainment by mutually interacting double toroidal vortex pairs and turbulent mixing

Boundary Contributions Using Fermion Pair Deformation

Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary contributions and demonstrate calculations using two examples, i.e, the standard QCD and deformed QCD with anomalous magnetic momentum coupling. As a by-product, we have extended BCFW recursion relation to off-shell gluon current, where because off-shell gluon current is not gauge invariant, a new feature must be cooperated.Comment: 26 pages, 4 figure

Heavy fermions and two loop electroweak corrections to b→s+γb\rightarrow s+\gamma

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+\gamma$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of $B\rightarrow X_{_s}\gamma$ can reach 5% as the energy scale of new physics $\Lambda_{_{\rm NP}}=200$ GeV.Comment: 30 pages,4 figure

No triangles on the moduli space of maximally supersymmetric gauge theory

Maximally supersymmetric gauge theory in four dimensions has a remarkably simple S-matrix at the origin of its moduli space at both tree and loop level. This leads to the question what, if any, of this structure survives at the complement of this one point. Here this question is studied in detail at one loop for the branch of the moduli space parameterized by a vacuum expectation value for one complex scalar. Motivated by the parallel D-brane picture of spontaneous symmetry breaking a simple relation is demonstrated between the Lagrangian of broken super Yang-Mills theory and that of its higher dimensional unbroken cousin. Using this relation it is proven both through an on- as well as an off-shell method there are no so-called triangle coefficients in the natural basis of one-loop functions at any finite point of the moduli space for the theory under study. The off-shell method yields in addition absence of rational terms in a class of theories on the Coulomb branch which includes the special case of maximal supersymmetry. The results in this article provide direct field theory evidence for a recently proposed exact dual conformal symmetry motivated by the AdS/CFT correspondence.Comment: 39 pages, 4 figure

On BCFW shifts of integrands and integrals

In this article a first step is made towards the extension of Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to arbitrary loop order. Surprisingly, it is shown that the large BCFW shift limit of the integrands has the same structure as the corresponding tree level amplitude in any minimally coupled Yang-Mills theory in four or more dimensions. This implies that these integrands can be reconstructed from a subset of their `single cuts'. The main tool is powercounting Feynman graphs in a special lightcone gauge choice employed earlier at tree level by Arkani-Hamed and Kaplan. The relation between shifts of integrands and shifts of its integrals is investigated explicitly at one loop. Two particular sources of discrepancy between the integral and integrand are identified related to UV and IR divergences. This is cross-checked with known results for helicity equal amplitudes at one loop. The nature of the on-shell residue at each of the single-cut singularities of the integrand is commented upon. Several natural conjectures and opportunities for further research present themselves.Comment: 43 pages, 6 figures, v2: minor improvement in exposition, typos fixed, bibliography update

Hierarchies of Susy Splittings and Invisible Photinos as Dark Matter

We explore how to generate hierarchies in the splittings between superpartners. Some of the consequences are the existence of invisible components of dark matter, new inflaton candidates, invisible monopoles and a number of invisible particles that might dominate during various eras, in particular between BBN and recombination and decay subsequently.Comment: 16 pages. v3: Ref. 27 has been modified. v4: Published versio

Two-step stabilization of orbital order and the dynamical frustration of spin in the model charge-transfer insulator KCuF3

We report a combined experimental and theoretical study of KCuF3, which offers - because of this material's relatively simple lattice structure and valence configuration (d9, i.e., one hole in the d-shell) - a particularly clear view of the essential role of the orbital degree of freedom in governing the dynamical coupling between the spin and lattice degrees of freedom. We present Raman and x-ray scattering evidence that the phase behaviour of KCuF3 is dominated above the Neel temperature (T_N = 40 K) by coupled orbital/lattice fluctuations that are likely associated with rotations of the CuF6 octahedra, and we show that these orbital fluctuations are interrupted by a static structural distortion that occurs just above T_N. A detailed model of the orbital and magnetic phases of KCuF3 reveals that these orbital fluctuations - and the related frustration of in-plane spin-order-are associated with the presence of nearly degenerate low-energy spin-orbital states that are highly susceptible to thermal fluctuations over a wide range of temperatures. A striking implication of these results is that the ground state of KCuF3 at ambient pressure lies near a quantum critical point associated with an orbital/spin liquid phase that is obscured by emergent Neel ordering of the spins; this exotic liquid phase might be accessible via pressure studies.Comment: 13 pages, 3 figure

The Hilbert Series of the One Instanton Moduli Space

The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.Comment: 43 pages, 22 figure

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure

De Sitter ground state of scalar-tensor gravity and its primordial perturbation

Scalar-tensor gravity is one of the most competitive gravity theory to Einstein's relativity. We reconstruct the exact de Sitter solution in scalar-tensor gravity, in which the non-minimal coupling scalar is rolling along the potential. This solution may have some relation to the early inflation and present acceleration of the universe. We investigated its primordial quantum perturbation around the adiabatic vacuum. We put forward for the first time that exact de Sitter generates non-exactly scale invariant perturbations. In the conformal coupling case, this model predicts that the tensor mode of the perturbation (gravity wave) is strongly depressed.Comment: 9 page