Asymmetric hypersonic flow

A general method for the analysis of the inviscid asymmetric hypersonic flow fields enveloping smooth bodies of general shape is given. The method is based on the assumption of a thin shock layer which yields an expression for pressure in generalized Mises coordinates. Numerical results for elliptic cones at angle of attack are shown to compare well with experiments and other theories. The computing logic for a blunt body is described, and a limiting solution at the stagnation point is presented

Inviscid flow about blunted cones of large opening angle at angle of attack

Application of a general method for calculation of inviscid hypersonic flow fields is discussed. General considerations are analyzed along with the sonic corner and the stagnation region. It is concluded that the complications caused by the requirement for sonic flow at the rear corner and particularly by the uncertain position of the stagnation streamline lead to sufficient difficulties with convergence of iterations that a practical procedure is not likely to be found

Development of a method of analysis and computer program for calculating the inviscid flow about the windward surfaces of space shuttle configurations at large angles of attack

A general method developed for the analysis of inviscid hypersonic shock layers is discussed for application to the case of the shuttle vehicle at high (65 deg) angle of attack. The associated extensive subsonic flow region caused convergence difficulties whose resolution is discussed. It is required that the solution be smoother than anticipated

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur

Falkner-Skan Flow Over a Wedge with Slip Boundary Conditions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76718/1/AIAA-2009-476-210.pd

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure

Structure of the fanconi anaemia monoubiquitin ligase complex

The Fanconi anaemia (FA) pathway repairs DNA damage caused by endogenous and chemotherapy-induced DNA crosslinks, and responds to replication stress1,2. Genetic inactivation of this pathway by mutation of genes encoding FA complementation group (FANC) proteins impairs development, prevents blood production and promotes cancer1,3. The key molecular step in the FA pathway is the monoubiquitination of a pseudosymmetric heterodimer of FANCD2-FANCI4,5 by the FA core complex-a megadalton multiprotein E3 ubiquitin ligase6,7. Monoubiquitinated FANCD2 then recruits additional protein factors to remove the DNA crosslink or to stabilize the stalled replication fork. A molecular structure of the FA core complex would explain how it acts to maintain genome stability. Here we reconstituted an active, recombinant FA core complex, and used cryo-electron microscopy and mass spectrometry to determine its structure. The FA core complex comprises two central dimers of the FANCB and FA-associated protein of 100 kDa (FAAP100) subunits, flanked by two copies of the RING finger subunit, FANCL. These two heterotrimers act as a scaffold to assemble the remaining five subunits, resulting in an extended asymmetric structure. Destabilization of the scaffold would disrupt the entire complex, resulting in a non-functional FA pathway. Thus, the structure provides a mechanistic basis for the low numbers of patients with mutations in FANCB, FANCL and FAAP100. Despite a lack of sequence homology, FANCB and FAAP100 adopt similar structures. The two FANCL subunits are in different conformations at opposite ends of the complex, suggesting that each FANCL has a distinct role. This structural and functional asymmetry of dimeric RING finger domains may be a general feature of E3 ligases. The cryo-electron microscopy structure of the FA core complex provides a foundation for a detailed understanding of its E3 ubiquitin ligase activity and DNA interstrand crosslink repair

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package