Clifford algebras and universal sets of quantum gates

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR

Razor clam to RoboClam: burrowing drag reduction mechanisms and their robotic adaptation

Estimates based on the strength, size, and shape of the Atlantic razor clam (Ensis directus) indicate that the animal's burrow depth should be physically limited to a few centimeters; yet razor clams can dig as deep as 70 cm. By measuring soil deformations around burrowing E. directus, we have found the animal reduces drag by contracting its valves to initially fail, and then fluidize, the surrounding substrate. The characteristic contraction time to achieve fluidization can be calculated directly from soil properties. The geometry of the fluidized zone is dictated by two commonly-measured geotechnical parameters: coefficient of lateral earth pressure and friction angle. Calculations using full ranges for both parameters indicate that the fluidized zone is a local effect, occurring between 1–5 body radii away from the animal. The energy associated with motion through fluidized substrate—characterized by a depth-independent density and viscosity—scales linearly with depth. In contrast, moving through static soil requires energy that scales with depth squared. For E. directus, this translates to a 10X reduction in the energy required to reach observed burrow depths. For engineers, localized fluidization offers a mechanically simple and purely kinematic method to dramatically reduce energy costs associated with digging. This concept is demonstrated with RoboClam, an E. directus-inspired robot. Using a genetic algorithm to find optimal digging kinematics, RoboClam has achieved localized fluidization burrowing performance comparable to that of the animal, with a linear energy-depth relationship, in both idealized granular glass beads and E. directus' native cohesive mudflat habitat.Battelle Memorial InstituteBluefin RoboticsChevron Corporatio

Quantum Approach to a Derivation of the Second Law of Thermodynamics

We re-interprete the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas-subsystem" under consideration and its environment ("container"). The time-average of a purity-measure is found to equal the average over the respective path in Hilbert-space. We then show that for typical (degenerate or non-degenerate) thermodynamical systems almost all states within the allowed region of Hilbert-space have a local von Neumann-entropy S close to the maximum and a purity P close to its minimum, respectively. Typically thermodynamical systems should therefore obey the second law.Comment: 4 pages. Accepted for publication in Phys. Rev. Let

NanoSIMS results from olivine-hosted melt embayments: Magma ascent rate during explosive basaltic eruptions

The explosivity of volcanic eruptions is governed in part by the rate at which magma ascends and degasses. Because the time scales of eruptive processes can be exceptionally fast relative to standard geochronometers, magma ascent rate remains difficult to quantify. Here we use as a chronometer concentration gradients of volatile species along open melt embayments within olivine crystals. Continuous degassing of the external melt during magma ascent results in diffusion of volatile species from embayment interiors to the bubble located at their outlets. The novel aspect of this study is the measurement of concentration gradients in five volatile elements (CO2, H2O, S, Cl, F) at fine-scale (5–10 μm) using the NanoSIMS. The wide range in diffusivity and solubility of these different volatiles provides multiple constraints on ascent timescales over a range of depths. We focus on four 100–200 μm, olivine-hosted embayments erupted on October 17, 1974 during the sub-Plinian eruption of Volcán de Fuego. H2O, CO2, and S all decrease toward the embayment outlet bubble, while F and Cl increase or remain roughly constant. Compared to an extensive melt inclusion suite from the same day of the eruption, the embayments have lost both H2O and CO2 throughout the entire length of the embayment. We fit the profiles with a 1-D numerical diffusion model that allows varying diffusivities and external melt concentrations as a function of pressure. Assuming a constant decompression rate from the magma storage region at approximately 220 MPa to the surface, H2O, CO2 and S profiles for all embayments can be fit with a relatively narrow range in decompression rates of 0.3–0.5 MPa/s, equivalent to 11–17 m/s ascent velocity and an 8 to 12 minute duration of magma ascent from ~ 10 km depth. A two stage decompression model takes advantage of the different depth ranges over which CO2 and H2O degas, and produces good fits given an initial stage of slow decompression (0.05–0.3 MPa/s) at high pressure (< 145 MPa), with similar decompression rates to the single-stage model for the shallower stage. The magma ascent rates reported here are among the first for explosive basaltic eruptions and demonstrate the potential of the embayment method for quantifying magmatic timescales associated with eruptions of different vigor

Multi-Substrate Burrowing Performance and Constitutive Modeling of RoboClam: A Biomimetic Robot Based on Razor Clams

The Atlantic razor clam (Ensis directus) reduces burrowing drag by using motions of its shell to fluidize a thin layer of substrate around its body. We have developed RoboClam, a robot that digs using the same mechanisms as Ensis, to explore how localized fluidization burrowing can be extended to engineering applications. In this work we present burrowing performance results of RoboClam in two distinctly different substrates: ideally granular 1mm soda lime glass beads and cohesive ocean mudflat soil. Using a genetic algorithm to optimize RoboClam’s kinematics, the machine was able to burrow in both substrates with a power law relationship between digging energy and depth of n = 1.17. Pushing through static soil has a theoretical energy-depth power law of n = 2, which means that Ensis-inspired burrowing motions can provide exponentially higher energy efficiency. We propose a theoretical constitutive model that describes how a fluidized region should form around a contracting body in virtually any type of saturated soil. The model predicts fluidization to be a relatively local effect, extending only two to three characteristic lengths away from the body, depending on friction angle and coefficient of lateral earth pressure, two commonly measured soil parameters.Battelle Memorial InstituteBluefin RoboticsChevron Corporatio

Full-lifetime simulations of multiple unequal-mass planets across all phases of stellar evolution

We know that planetary systems are just as common around white dwarfs as around main-sequence stars. However, self-consistently linking a planetary system across these two phases of stellar evolution through the violent giant branch poses computational challenges, and previous studies restricted architectures to equal-mass planets. Here, we remove this constraint and perform over 450 numerical integrations over a Hubble time (14 Gyr) of packed planetary systems with unequal-mass planets. We characterize the resulting trends as a function of planet order and mass. We find that intrusive radial incursions in the vicinity of the white dwarf become less likely as the dispersion amongst planet masses increases. The orbital meandering which may sustain a sufficiently dynamic environment around a white dwarf to explain observations is more dependent on the presence of terrestrial-mass planets than any variation in planetary mass. Triggering unpacking or instability during the white dwarf phase is comparably easy for systems of unequal-mass planets and systems of equal-mass planets; instabilities during the giant branch phase remain rare and require fine-tuning of initial conditions. We list the key dynamical features of each simulation individually as a potential guide for upcoming discoveries

Urinary biomarker concentrations of captan, chlormequat, chlorpyrifos and cypermethrin in UK adults and children living near agricultural land

There is limited information on the exposure to pesticides experienced by UK residents living near agricultural land. This study aimed to investigate their pesticide exposure in relation to spray events. Farmers treating crops with captan, chlormequat, chlorpyrifos or cypermethrin provided spray event information. Adults and children residing ≤100 m from sprayed fields provided first-morning void urine samples during and outwith the spray season. Selected samples (1–2 days after a spray event and at other times (background samples)) were analysed and creatinine adjusted. Generalised Linear Mixed Models were used to investigate if urinary biomarkers of these pesticides were elevated after spray events. The final data set for statistical analysis contained 1518 urine samples from 140 participants, consisting of 523 spray event and 995 background samples which were analysed for pesticide urinary biomarkers. For captan and cypermethrin, the proportion of values below the limit of detection was greater than 80%, with no difference between spray event and background samples. For chlormequat and chlorpyrifos, the geometric mean urinary biomarker concentrations following spray events were 15.4 μg/g creatinine and 2.5 μg/g creatinine, respectively, compared with 16.5 μg/g creatinine and 3.0 μg/g creatinine for background samples within the spraying season. Outwith the spraying season, concentrations for chlorpyrifos were the same as those within spraying season backgrounds, but for chlormequat, lower concentrations were observed outwith the spraying season (12.3 μg/g creatinine). Overall, we observed no evidence indicative of additional urinary pesticide biomarker excretion as a result of spray events, suggesting that sources other than local spraying are responsible for the relatively low urinary pesticide biomarkers detected in the study population