Beyond velocity and acceleration: Jerk, snap and higher derivatives

© 2016 IOP Publishing Ltd. The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts

Development of the Techology for Intermediate Energy Electron Cooling

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Study of the Feasibility of Decreasing the Emittance of the SSC Beam Through the Use of Electron Cooling in the SSC Medium Energy Booster

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Design of a 6 MeV Electron Cooling System for the SSC Medium Energy Booster

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Results from the intercalibration of optical low light calibration sources 2011

Following the 38th Annual European Meeting on Atmospheric Studies by Optical Methods in Siuntio in Finland, an intercalibration workshop for optical low light calibration sources was held in Sodankylä, Finland. The main purpose of this workshop was to provide a comparable scale for absolute measurements of aurora and airglow. All sources brought to the intercalibration workshop were compared to the Fritz Peak reference source using the Lindau Calibration Photometer built by Wilhelm Barke and Hans Lauche in 1984. The results were compared to several earlier intercalibration workshops. It was found that most sources were fairly stable over time, with errors in the range of 5–25%. To further validate the results, two sources were also intercalibrated at UNIS, Longyearbyen, Svalbard. Preliminary analysis indicates agreement with the intercalibration in Sodankylä within about 15–25%

The Beam Transfer Function Experiments: CE-37

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Efficient Bit-Decomposition and Modulus-Conversion Protocols with an Honest Majority

We propose secret-sharing-based bit-decomposition and modulus conversion protocols for a prime order ring $\mathbb{Z}_p$ with an honest majority: an adversary can corrupt $k-1$ parties of $n$ parties and $2k-1 \le n$. Our protocols are secure against passive and active adversaries depending on the components of our protocols. We assume a secret is an $\ell$-bit element and $2^{\ell+\lceil \log m \rceil} < p$, where $m= k$ in the passive security and $m= \binom{n}{k-1}$ in the active security. The outputs of our bit-decomposition and modulus-conversion protocols are $\ell$ tuple of shares in $\mathbb{Z}_2$ and a share in $\mathbb{Z}_{p\u27}$, respectively, where $p\u27$ is the modulus to be converted. If $k$ and $n$ are small, the communication complexity of our passively secure bit-decomposition and modulus-conversion protocols are $O(\ell)$ bits and $O(\lceil \log p\u27 \rceil)$ bits, respectively. Our key observation is that a quotient of additive shares can be computed from the \emph{least} significant $\lceil \log m \rceil$ bits. If a secret $a$ is ``shifted\u27\u27 and additively shared by $x_i$ in $\mathbb{Z}_p$ as $2^{\lceil \log m \rceil}a = \sum_{i=0}^{m-1} x_i = 2^{ \lceil \log m \rceil} a + qp$, the least significant $\lceil \log m \rceil$ bits of $\sum_{i=0}^{m-1} x_i$ determines $q$ since $p$ is an odd prime and the least significant $\lceil \log m \rceil$ bits of $2^{\lceil \log m \rceil} a$ are $0$s

Amortised Memory Analysis Using the Depth of Data Structures

Abstract. Hofmann and Jost have presented a heap space analysis [1] that finds linear space bounds for many functional programs. It uses an amortised analysis: assigning hypothetical amounts of free space (called potential) to data structures in proportion to their sizes using type annotations. Constraints on these annotations in the type system ensure that the total potential assigned to the input is an upper bound on the total memory required to satisfy all allocations. We describe a related system for bounding the stack space requirements which uses the depth of data structures, by expressing potential in terms of maxima as well as sums. This is achieved by adding extra structure to typing contexts (inspired by O’Hearn’s bunched typing [2]) to describe the form of the bounds. We will also present the extra steps that must be taken to construct a typing during the analysis. Obtaining bounds on the resource requirements of programs can be crucial for ensuring that they enjoy reliability and security properties, particularly for use i

The Acceleration and Storage of Radioactive Ions for a Beta-Beam Facility

The term beta-beam has been coined for the production of a pure beam of electron neutrinos or their antiparticles through the decay of radioactive ions circulating in a storage ring. This concept requires radioactive ions to be accelerated to as high Lorentz gamma as 150. The neutrino source itself consists of a storage ring for this energy range, with long straight sections in line with the experiment(s). Such a decay ring does not exist at CERN today, nor does a high-intensity proton source for the production of the radioactive ions. Nevertheless, the existing CERN accelerator infrastructure could be used as this would still represent an important saving for a beta-beam facility.Comment: beta-beam working group website at http://cern.ch/beta-bea