Branch Folding Research Articles

Ginzburg–Landau model of a Stiffnessometer — A superconducting stiffness meter device

We study the Ginzburg–Landau equations of super-conductivity describing the experimental setup of a Stiffnessometer device. In particular, we consider the nonlinear regime which reveals the impact of the superconductive critical current on the Stiffnessometer signal. As expected, we find that at high flux regimes, superconductivity is destroyed in parts of the superconductive region. Surprisingly, however, we find that the superconductivity does not gradually decay to zero as flux increases, but rather the branch of solutions undergoes branch folding. We use asymptotic analysis to characterize the solutions at the numerous parameter regimes in which they exist. An immediate application of the work is an extension of the regime in which experimental measurements of the Stiffnessometer device can be interpreted.

Dispersion analysis with 45°-rotated augmented supercells and applications in phononic crystal design

The supercell approach can be useful for tailoring dispersion curves of phononic crystals, but the interpretation of the dispersion curves in the supercells can be often intriguing. Supercells formed by integer multiples of an original unit cell along its lattice axes are common, but there are also important situations requiring supercells formed by non-integer multiples of an original unit cell and its rotation with respect to its lattice axes. In these cases, not only dispersion branch folding, but also branch overlapping not found in common supercells, take place, which complicates the correct interpretation of band structures. In this study, we consider 45°-rotated augmented supercells and analyze why and how branch folding and overlapping take place. For the analysis, the relation between the first Brillouin zone of an original cell and that of the corresponding 45°-rotated augmented supercell is investigated. The analysis of the folding and overlapping mechanism found in the dispersion curve of the supercell is also useful for interpreting which branches can be excited over a target wavevector direction. The usefulness of the findings of this supercell-based dispersion analysis is demonstrated in unit cell design problems. Specifically, we show how to interpret correctly the dispersion curves of phononic crystals made of unit cells optimized by bandgap maximizing topology optimization when the optimized unit cells turn out to be 45°-rotated augmented supercells. Conversely, throughout design optimization iterations, the original period of a unit cell that is initially set at the beginning of design optimization can be maintained if branch overlapping is forced not to occur.

Raman spectra and structural peculiarities of GaAs nanowires

The Raman scattering spectra of nanowire samples in the region of fundamental modes (50–320 cm−1) are studied to analyze the structural peculiarities of GaAs nanowires (nanowhiskers) grown on a Si (111) substrate. Factor analysis of the experimental data array consisting of 55 spectra, each of which contains 300 points, is carried out. It is found that the number of linearly independent contributions in these data arrays amounts to only two spectra. The form of each linearly independent contribution is close to zincblende (ZB) and wurtzite (WZ) spectra. It is established that ZB and WZ phases exist in nanowhiskers. Comparison with the calculated frequencies of the normal vibrations of hexagonal GaAs polytypes makes it possible to assume that the spectra of crystal nanowhiskers are combinations of ZB and WZ spectra with good accuracy and agree with the scheme of phonon branch folding of the ZB Brillouin zone.

Reconstructing a lost world: Ediacaran rangeomorphs from Spaniard's Bay, Newfoundland

Ediacaran fronds at Spaniard's Bay on the Avalon Peninsula of Newfoundland exhibit exquisite, three-dimensional preservation with morphological features less than 0.05 mm in width visible on the best preserved specimens. Most of the nearly 100 specimens are juvenile rangeomorphs, an extinct Ediacaran clade that numerically dominated the early evolution of complex multicellular life. Spaniard's Bay rangeomorphs are characterized by cm-scale architectural elements exhibiting self-similar branching over several fractal scales that were used as modules in construction of larger structures. Four taxa of rangeomorph fronds are present – Avalofractus abaculus n. gen. et sp., Beothukis mistakensis Brasier and Antcliffe, Trepassia wardae (Narbonne and Gehling), and Charnia cf. C. masoni Ford. All of these taxa exhibit an alternate array of primary rangeomorph branches that pass off a central stalk or furrow that marks the midline of the petalodium. Avalofractus is remarkably self similar over at least four fractal scales, with each scale represented by double-sided rangeomorph elements that were constrained only at their attachment point with the higher-order branch and thus were free to rotate and pivot relative to other branches. Beothukis is similar in organization, but its primary branches show only one side of a typical rangeomorph element, probably due to longitudinal branch folding, and the position of the individual branches was moderately constrained. Trepassia shows only single-sided branches with both primary and secondary branches emanating from a central stalk or furrow; primary branches were capable of minor pivoting as reflected in bundles of secondary branches. Charnia shows only single-sided primary branches that branch from a zigzag central furrow and that were firmly constrained relative to each. This sequence provides a developmental linkage between Rangea-type and Charnia-type rangeomorphs. Avalonian assemblages show a wide array of rangeomorph constructions, but later Ediacaran assemblages contain a lower diversity of rangeomorphs represented mainly by well-constrained forms.

A study on the transmission of picosecond ultrasonic waves in Si∕Mo superlattices

We have performed theoretical and experimental studies on the optical generation and transmission of picosecond ultrasonic pulses in a-Si∕Mo superlattices using ultrafast lasers. The pulse shapes and spectra of collectively excited folded phonon waves were analyzed. Calculations show that the picosecond strain pulses transmitted through a superlattice have a very complicated waveform due to branch folding and phononic bandgaps, but the transient piezoreflectance (TPR) response has a rather simple shape, similar to that of a homogeneous thin film. A direct pulse-echo technique was used to measure the waveform of the TPR response and the effective sound velocity of the folded phonons. The experimental results agree well with the theoretical predictions.

Complexation of Cu(II) Ions with the Lowest Generation Poly(amido-amine)-OH Dendrimers: A Molecular Simulation Study

Classical molecular dynamics simulations and density functional theory calculations are performed to obtain insights about the attachment of the copper(II) ion to the lowest generation poly(amido-amine) dendrimer, G0-OH, in aqueous solutions. Various initial configurations of the ion relative to the dendrimer sites are tested and it is concluded that both the solvent as well as-in a lesser degree for low generation dendrimers-the folding of the dendrimer branch play an important role in copper(II) ion complexation. The presence of solvent and branch folding retain the ion close to the atomic binding sites consisting mainly of amide oxygen as well as hydroxyl oxygen but also tertiary amine nitrogen. A discussion of currently available experimental results in Cu(II) complexation in larger generation dendrimers is provided.

Speculative Branch Folding for Pipelined Processors

This paper proposes an effective branch folding technique which combines branch instructions with predicted instructions. This technique can be implemented using an instruction queue, which buffers prefetched instructions. Most of the instructions in the instruction queue are forwarded to the execution unit in sequence. Branch instructions, however, are combined with predicted instructions in the instruction queue and these folded instructions are forwarded to the execution unit. Miss-prediction can be recovered by flushing folded instructions without processor state recovery and by restarting from the other path. Simulation and implementation results show that both performance and power consumption are significantly improved with little additional hardware cost.

Cobalt: A Language for Writing Provably-Sound Compiler Optimizations

We overview the current status and future directions of the Cobalt project. Cobalt is a domain-specific language for implementing compiler optimizations as guarded rewrite rules. Cobalt optimizations operate over a C-like intermediate representation including unstructured control flow, pointers to local variables and dynamically allocated memory, and recursive procedures. The design of Cobalt engenders a natural inductive strategy for proving the soundness of optimizations. This strategy is fully automated by requiring an automatic theorem prover to discharge a small set of simple proof obligations for each optimization. We have written a variety of forward and backward intraprocedural dataflow optimizations in Cobalt, including constant propagation and folding, branch folding, full and partial redundancy elimination, full and partial dead assignment elimination, and simple forms of points-to analysis. The implementation of our soundness-checking strategy employs the Simplify automatic theorem prover, and we have used this implementation to automatically prove the above optimizations correct. An execution engine for Cobalt optimizations is implemented as part of the Whirlwind compiler infrastructure.

Picosecond X-Ray Studies of Coherent Folded Acoustic Phonons in a Multiple Quantum Well

Coherent folded acoustic phonons in a multilayered GaSb/InAs epitaxial heterostructure were generated by femtosecond laser pulses and studied by means of ultrafast x-ray diffraction. Coherent phonons excited simultaneously in the fundamental acoustic branch and the first back-folded branch were detected. This represents the first clear evidence for phonon branch folding based directly on the atomic motion to which x-ray diffraction is sensitive. From a comparison of the measured phonon-modulated x-ray reflectivity with simulations, evidence was found for a reduction of the laser penetration depth. This reduction can be explained by the self-modulation of the refractive index due to photogenerated free carriers.

Automatically proving the correctness of compiler optimizations

We describe a technique for automatically proving compiler optimizations sound , meaning that their transformations are always semantics-preserving. We first present a domain-specific language, called Cobalt, for implementing optimizations as guarded rewrite rules. Cobalt optimizations operate over a C-like intermediate representation including unstructured control flow, pointers to local variables and dynamically allocated memory, and recursive procedures. Then we describe a technique for automatically proving the soundness of Cobalt optimizations. Our technique requires an automatic theorem prover to discharge a small set of simple, optimization-specific proof obligations for each optimization. We have written a variety of forward and backward intraprocedural dataflow optimizations in Cobalt, including constant propagation and folding, branch folding, full and partial redundancy elimination, full and partial dead assignment elimination, and simple forms of points-to analysis. We implemented our soundness-checking strategy using the Simplify automatic theorem prover, and we have used this implementation to automatically prove our optimizations correct. Our checker found many subtle bugs during the course of developing our optimizations. We also implemented an execution engine for Cobalt optimizations as part of the Whirlwind compiler infrastructure.

Reducing the branch penalty in pipelined processors

A probabilistic model is developed to quantify the performance effects of the branch penalty in a typical pipeline. The branch penalty is analyzed as a function of the relative number of branch instructions executed and the probability that a branch is taken. The resulting model shows the fraction of maximum performance achievable under the given conditions. Techniques to reduce the branch penalty include static and dynamic branch prediction, the branch target buffer, the delayed branch, branch bypassing and multiple prefetching, branch folding, resolution of branch decision early in the pipeline, using multiple independent instruction streams in a shared pipeline, and the prepare-to-branch instruction.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>