Regularly spaced subsums of integer partitions

For integer partitions $\lambda :n=a_1+...+a_k$, where $a_1\ge a_2\ge >...\ge a_k\ge 1$, we study the sum $a_1+a_3+...$ of the parts of odd index. We show that the average of this sum, over all partitions $\lambda$ of $n$, is of the form $n/2+(\sqrt{6}/(8\pi))\sqrt{n}\log{n}+c_{2,1}\sqrt{n}+O(\log{n}).$ More generally, we study the sum $a_i+a_{m+i}+a_{2m+i}+...$ of the parts whose indices lie in a given arithmetic progression and we show that the average of this sum, over all partitions of $n$, is of the form $n/m+b_{m,i}\sqrt{n}\log{n}+c_{m,i}\sqrt{n}+O(\log{n})$, with explicitly given constants $b_{m,i},c_{m,i}$. Interestingly, for $m$ odd and $i=(m+1)/2$ we have $b_{m,i}=0$, so in this case the error term is of lower order. The methods used involve asymptotic formulas for the behavior of Lambert series and the Zeta function of Hurwitz. We also show that if $f(n,j)$ is the number of partitions of $n$ the sum of whose parts of even index is $j$, then for every $n$, $f(n,j)$ agrees with a certain universal sequence, Sloane's sequence \texttt{#A000712}, for $j\le n/3$ but not for any larger $j$

Heavy Quark Fragmentation to Baryons Containing Two Heavy Quarks

We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass $m_Q\gg\Lambda_{\rm QCD}$. In this limit the heavy quarks first combine perturbatively into a compact diquark with a radius small compared to $1/\Lambda_{\rm QCD}$, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this $QQ$ diquark to a $QQq$ baryon is identical to the fragmentation of a heavy antiquark to a meson. We apply this analysis to the production of baryons of the form $ccq$, $bbq$, and $bcq$.Comment: 9 pages, 1 figure included, uses harvmac.tex and epsf.tex, UCSD/PTH 93-11, CALT-68-1868, SLAC-PUB-622

Heap Formation in Granular Media

Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems, heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9

Calibration of the LIGO displacement actuators via laser frequency modulation

We present a frequency modulation technique for calibration of the displacement actuators of the LIGO 4-km-long interferometric gravitational-wave detectors. With the interferometer locked in a single-arm configuration, we modulate the frequency of the laser light, creating an effective length variation that we calibrate by measuring the amplitude of the frequency modulation. By simultaneously driving the voice coil actuators that control the length of the arm cavity, we calibrate the voice coil actuation coefficient with an estimated 1-sigma uncertainty of less than one percent. This technique enables a force-free, single-step actuator calibration using a displacement fiducial that is fundamentally different from those employed in other calibration methods.Comment: 10 pages, 5 figures, submitted to Classical and Quantum Gravit

On Characterizing the Data Access Complexity of Programs

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a fundamental characterization of data access complexity will be increasingly important. The problem of developing lower bounds for data access complexity has been modeled using the formalism of Hong & Kung's red/blue pebble game for computational directed acyclic graphs (CDAGs). However, previously developed approaches to lower bounds analysis for the red/blue pebble game are very limited in effectiveness when applied to CDAGs of real programs, with computations comprised of multiple sub-computations with differing DAG structure. We address this problem by developing an approach for effectively composing lower bounds based on graph decomposition. We also develop a static analysis algorithm to derive the asymptotic data-access lower bounds of programs, as a function of the problem size and cache size

Neurogenic Fever after Acute Traumatic Spinal Cord Injury: A Qualitative Systematic Review.

STUDY DESIGN: Systematic review. OBJECTIVE: To determine the incidence, pathogenesis, and clinical outcomes related to neurogenic fevers following traumatic spinal cord injury (SCI). METHODS: A systematic review of the literature was performed on thermodysregulation secondary to acute traumatic SCI in adult patients. A literature search was performed using PubMed (MEDLINE), Cochrane Central Register of Controlled Trials, and Scopus. Using strict inclusion and exclusion criteria, seven relevant articles were obtained. RESULTS: The incidence of fever of all origins (both known and unknown) after SCI ranged from 22.5 to 71.7% with a mean incidence of 50.6% and a median incidence of 50.0%. The incidence of fever of unknown origin (neurogenic fever) ranged from 2.6 to 27.8% with a mean incidence of 8.0% and a median incidence of 4.7%. Cervical and thoracic spinal injuries were more commonly associated with fever than lumbar injuries. In addition, complete injuries had a higher incidence of fever than incomplete injuries. The pathogenesis of neurogenic fever after acute SCI is not thoroughly understood. CONCLUSION: Neurogenic fevers are relatively common following an acute SCI; however, there is little in the scientific literature to help physicians prevent or treat this condition. The paucity of research underscored by this review demonstrates the need for further studies with larger sample sizes, focusing on incidence rate, clinical outcomes, and pathogenesis of neurogenic fever following acute traumatic SCI

Two scenarios for avalanche dynamics in inclined granular layers

We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let

Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles

We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.Comment: 14 pages, Plain Te

Low-Altitude Reconnection Inflow-Outflow Observations during a 2010 November 3 Solar Eruption

For a solar flare occurring on 2010 November 3, we present observations using several SDO/AIA extreme-ultraviolet (EUV) passbands of an erupting flux rope followed by inflows sweeping into a current sheet region. The inflows are soon followed by outflows appearing to originate from near the termination point of the inflowing motion - an observation in line with standard magnetic reconnection models. We measure average inflow plane-of-sky speeds to range from ~150-690 km/s with the initial, high-temperature inflows being the fastest. Using the inflow speeds and a range of Alfven speeds, we estimate the Alfvenic Mach number which appears to decrease with time. We also provide inflow and outflow times with respect to RHESSI count rates and find that the fast, high-temperature inflows occur simultaneously with a peak in the RHESSI thermal lightcurve. Five candidate inflow-outflow pairs are identified with no more than a minute delay between detections. The inflow speeds of these pairs are measured to be 10^2 km/s with outflow speeds ranging from 10^2-10^3 km/s - indicating acceleration during the reconnection process. The fastest of these outflows are in the form of apparently traveling density enhancements along the legs of the loops rather than the loop apexes themselves. These flows could either be accelerated plasma, shocks, or waves prompted by reconnection. The measurements presented here show an order of magnitude difference between the retraction speeds of the loops and the speed of the density enhancements within the loops - presumably exiting the reconnection site.Comment: 31 pages, 13 figures, 1 table, Accepted to ApJ (expected publication ~July 2012