Orbit determination and control for the European Student Moon Orbiter

Scheduled for launch in 2014-2015 the European Student Moon Orbiter (ESMO) will be the first lunar microsatellite designed entirely by the student population. ESMO is being developed through the extensive use of flight spared and commercial of the shelf units. As such ESMO is significantly constrained by the available mission delta-V. This provides a considerable challenge in designing a viable transfer and stable orbit around the Moon. Coupled with an all-day piggy-back launch opportunity, where ESMO has little or no control over the launch date, ESMO is considered to be an ambitious design. To overcome these inherent challenges, the use of a Weak Stability Boundary (WSB) transfer into a highly eccentric orbit is proposed. However to ensure accurate insertion around the Moon, ESMO must use a complex navigation strategy. This includes mitigation approaches and correction strategies. This paper will therefore present results from the ongoing orbit determination analysis and navigation scenarios to ensure capture around the Moon. While minimising the total delta-V, analysis includes planning for orbital control, scheduling and the introduction of Trajectory Correction Manoeuvres (TCMs). Analysis was performed for different transfer options, final lunar orbit selection and available ground stations

First passage in an interval for fractional Brownian motion

Be $X_t$ a random process starting at $x \in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to $P_1'(x)=1$. For fractional Brownian motion with Hurst exponent $H$, we establish that $P_1'(x) = {\cal N} [x(1-x)]^{\frac1H -2} e^{\epsilon {\cal F}(x)+ {\cal O}(\epsilon^2)}$, where $\epsilon=H-\frac12$. The function ${\cal F}(x)$ is analytic, and well approximated by its Taylor expansion, ${\cal F}(x)\simeq 16 (C-1) (x-1/2)^2 +{\cal O}(x-1/2)^4$, where $C= 0.915...$ is the Catalan-constant. A similar result holds for moments of the exit time starting at $x$. We then consider the span of $X_t$, i.e. the size of the (compact) domain visited up to time $t$. For Brownian motion, we derive an analytic expression for the probability that the span reaches 1 for the first time, then generalized to fBm. Using large-scale numerical simulations with system sizes up to $N=2^{24}$ and a broad range of $H$, we confirm our analytic results. There are important finite-discretization corrections which we quantify. They are most severe for small $H$, necessitating to go to the large systems mentioned above.Comment: 21 pages, 54 figures. v2: additional material and clarifications adde

Efficient kinetic Monte Carlo method for reaction-diffusion processes with spatially varying annihilation rates

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.Comment: 13 pages, 5 figure

Perception of categories: from coding efficiency to reaction times

Reaction-times in perceptual tasks are the subject of many experimental and theoretical studies. With the neural decision making process as main focus, most of these works concern discrete (typically binary) choice tasks, implying the identification of the stimulus as an exemplar of a category. Here we address issues specific to the perception of categories (e.g. vowels, familiar faces, ...), making a clear distinction between identifying a category (an element of a discrete set) and estimating a continuous parameter (such as a direction). We exhibit a link between optimal Bayesian decoding and coding efficiency, the latter being measured by the mutual information between the discrete category set and the neural activity. We characterize the properties of the best estimator of the likelihood of the category, when this estimator takes its inputs from a large population of stimulus-specific coding cells. Adopting the diffusion-to-bound approach to model the decisional process, this allows to relate analytically the bias and variance of the diffusion process underlying decision making to macroscopic quantities that are behaviorally measurable. A major consequence is the existence of a quantitative link between reaction times and discrimination accuracy. The resulting analytical expression of mean reaction times during an identification task accounts for empirical facts, both qualitatively (e.g. more time is needed to identify a category from a stimulus at the boundary compared to a stimulus lying within a category), and quantitatively (working on published experimental data on phoneme identification tasks)

Probabilistic Description of Traffic Breakdowns

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, may be, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. The latter is justified using the available experimental data for the correlation properties of the synchronized mode. We write the appropriate master equation converted then into the Fokker-Plank equation for the cluster distribution function and analyze the formation of the critical car cluster due to the climb over a certain potential barrier. The further cluster growth irreversibly gives rise to the jam formation. Numerical estimates of the obtained characteristics and the experimental data of the traffic breakdown are compared. In particular, we draw a conclusion that the characteristic intrinsic time scale of the breakdown phenomenon should be about one minute and explain the case why the traffic volume interval inside which traffic breakdown is observed is sufficiently wide.Comment: RevTeX 4, 14 pages, 10 figure

A geostatistical model based on Brownian motion to Krige regions in R2 with irregular boundaries and holes

Master's Project (M.S.) University of Alaska Fairbanks, 2019Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries, inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R 2 . This model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data from Puget Sound

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.