Development of an orthotropic hole element

A finite element was developed which adequately represents the state of stress in the region around a circular hole in orthotropic material experiencing reasonably general loading. This was achieved with a complementary virtual work formulation of the stiffness and stress matrices for a square element with center circular hole. The assumed stress state provides zero shearing stress on the hole boundary, so the element is suitable for problems involving load transfer without friction. The element has been implemented in the NASTRAN computer program, and sample problem results are presented

Lateral Load Strength of Screw Connections in 29ga Metal

The results of 300 tests on screwed connections in shear are presented. The load capacity of screws in a row is shown to be additive and screws placed in narrow ribs of 29ga steel have the same strength as screws placed in flat sheets. The AISI equation for tilting strength of screw connections under predicts the strength of the screw connections tested. A regression equation is developed for tilting and compared to the AISI tilting equation and a third party test data. The regression equation is more accurate but less precise than the AISI equation

Time-dependent density functional theory on a lattice

A time-dependent density functional theory (TDDFT) for a quantum many-body system on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is $v$-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is $v$-representable and therefore the lattice TDDFT is guaranteed to exist. The TDDFT existence and uniqueness theorem is valid for any connected lattice, independently of its size, geometry and/or spatial dimensionality. The general statements of the existence theorem are illustrated on a pedagogical exactly solvable example which displays all details and subtleties of the proof in a transparent form. In conclusion we briefly discuss remaining open problems and directions for a future research.Comment: 12 pages, 1 figur

Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC

Previous work on electroweak radiative corrections to high energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to compute radiative corrections to all parton-level hard scattering amplitudes in the standard model to NLL order, including QCD and electroweak radiative corrections, mass effects, and Higgs exchange corrections, if the high-scale matching, which is suppressed by two orders in the log counting, and contains no large logs, is known. The factorization structure of the effective theory places strong constraints on the form of gauge theory amplitudes at high energy for massless and massive gauge theories, which are discussed in detail in the paper. The radiative corrections can be written as the sum of process-independent one-particle collinear functions, and a universal soft function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at 2 TeV for transverse W pair production, and increasing rapidly with energy. The estimated theoretical uncertainty to the partonic (hard) cross-section in most cases is below one percent, smaller than uncertainties in the parton distribution functions (PDFs). We discuss the relation between SCET and other factorization methods, and derive the Magnea-Sterman equations for the Sudakov form factor using SCET, for massless and massive gauge theories, and for light and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed because of a possible subtlet

Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/epsilon contributions, and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions 'minus' a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.Comment: 9 pages, 5 figures. V2:ref adde

Electroweak Corrections using Effective Field Theory: Applications to the LHC

Electroweak Sudakov logarithms at high energy, of the form alpha/sin^2 theta_W^n log^m s/M_{Z,W}^2, are summed using effective theory (EFT) methods. The exponentiation of Sudakov logarithms and factorization is discussed in the EFT formalism. Radiative corrections are computed to scattering processes in the standard model involving an arbitrary number of external particles. The computations include non-zero particle masses such as the t-quark mass, electroweak mixing effects which lead to unequal W and Z masses and a massless photon, and Higgs corrections proportional to the top quark Yukawa coupling. The structure of the radiative corrections, and which terms are summed by the EFT renormalization group is discussed in detail. The omitted terms are smaller than 1%. We give numerical results for the corrections to dijet production, dilepton production, t-\bar t production, and squark pair production. The purely electroweak corrections are significant -- about 15% at 1 TeV, increasing to 30% at 5 TeV, and they change both the scattering rate and angular distribution. The QCD corrections (which are well-known) are also computed with the EFT. They are much larger -- about a factor of four at 1 TeV, increasing to a factor of thirty at 5 TeV. Mass effects are also significant; the q \bar q -> t \bar t rate is enchanced relative to the light-quark production rate by 40%.Comment: Additional details added on exponentiation, and the form of the Sudakov series. Figures darkened to print better. 40 pages, 40 figure

The Mason-Alberta Phonetic Segmenter: A forced alignment system based on deep neural networks and interpolation

Forced alignment systems automatically determine boundaries between segments in speech data, given an orthographic transcription. These tools are commonplace in phonetics to facilitate the use of speech data that would be infeasible to manually transcribe and segment. In the present paper, we describe a new neural network-based forced alignment system, the Mason-Alberta Phonetic Segmenter (MAPS). The MAPS aligner serves as a testbed for two possible improvements we pursue for forced alignment systems. The first is treating the acoustic model in a forced aligner as a tagging task, rather than a classification task, motivated by the common understanding that segments in speech are not truly discrete and commonly overlap. The second is an interpolation technique to allow boundaries more precise than the common 10 ms limit in modern forced alignment systems. We compare configurations of our system to a state-of-the-art system, the Montreal Forced Aligner. The tagging approach did not generally yield improved results over the Montreal Forced Aligner. However, a system with the interpolation technique had a 27.92% increase relative to the Montreal Forced Aligner in the amount of boundaries within 10 ms of the target on the test set. We also reflect on the task and training process for acoustic modeling in forced alignment, highlighting how the output targets for these models do not match phoneticians' conception of similarity between phones and that reconciliation of this tension may require rethinking the task and output targets or how speech itself should be segmented.Comment: submitted for publicatio

Normalizations with exponentially small remainders for nonautonomous analytic periodic vector fields

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordinates in E1 allowing to eliminate up to a finite polynomial order all terms depending only on the coordinate u0 of E0 in the E1 component of the vector field. We moreover show that, optimizing the choice of the degree of the polynomial change of coordinates, we get an exponentially small remainder. In the second part, we prove a normal form theorem with exponentially small remainder. Similar theorems have been proved before in the autonomous case : this paper generalizes those results to the nonautonomous periodic case

Pseudo-transient Continuation, Solution Update Methods, and CFL Strategies for DG Discretizations of the RANS-SA Equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106459/1/AIAA2013-2686.pd