Light Transport in PT-invariant Photonic Structures with Hidden Symmetries

We introduce a recursive bosonic quantization technique for generating classical PT photonic structures that possess hidden symmetries and higher order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such PT-symmetric photonic networks is also presented.

ANKLE IMPEDANCE AND ANKLE ANGLES DURING STEP TURN AND STRAIGHT WALK: IMPLICATIONS FOR THE DESIGN OF A STEERABLE ANKLE-FOOT PROSTHETIC ROBOT

During locomotion, turning is a common and recurring event which is largely neglected in the current state-of-the-art ankle-foot prostheses, forcing amputees to use different steering mechanisms for turning, compared to non-amputees. A better understanding of the complexities surrounding lower limb prostheses will lead to increased health and well-being of amputees. The aim of this research is to develop a steerable ankle-foot prosthesis that mimics the human ankle mechanical properties. Experiments were developed to estimate the mechanical impedance of the ankle and the ankles angles during straight walk and step turn. Next, this information was used in the design of a prototype, powered steerable ankle-foot prosthesis with two controllable degrees of freedom. One of the possible approaches in design of the prosthetic robots is to use the human joints’ parameters, especially their impedance. A series of experiments were conducted to estimate the stochastic mechanical impedance of the human ankle when muscles were fully relaxed and co-contracting antagonistically. A rehabilitation robot for the ankle, Anklebot, was employed to provide torque perturbations to the ankle. The experiments were performed in two different configurations, one with relaxed muscles, and one with 10% of maximum voluntary contraction (MVC). Surface electromyography (sEMG) was used to monitor muscle activation levels and these sEMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the lateral/medial (LM) directions, inversion-eversion (IE), and dorsiflexionplantarflexion (DP) were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in all degrees of freedom of the ankle. Another experiment compared the three-dimensional angles of the ankle during step turn and straight walking. These angles were measured to be used for developing the control strategy of the ankle-foot prosthesis. An infrared camera system was used to track the trajectories and angles of the foot and leg. The combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The Range of motion (ROM) in IE increased during turning while ML rotation decreased and DP changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk and progressively showed less plantarflexion. In IE, the ankle showed increased inversion leaning the body toward the inside of the turn. ML rotation initiated with an increased medial rotation during the step turn relative to the straight walk transitioning to increased lateral rotation at the toe off. A prototype ankle-foot prosthesis capable of controlling both DP and IE using a cable driven mechanism was developed and assessed as part of a feasibility study. The design is capable of reproducing the angles required for straight walk and step turn; generates 712N of lifting force in plantarflexion, and shows passive stiffness comparable to a nonload bearing ankle impedance. To evaluate the performance of the ankle-foot prosthesis, a circular treadmill was developed to mimic human gait during steering. Preliminary results show that the device can appropriately simulate human gait with loading and unloading the ankle joint during the gait in circular paths.

Rotation Grazing Demonstrations With Beef Cows on HEL - Adams County Conservation Reserve Program (CRP) Project

Two grazing systems were demonstrated on Conservation Reserve Program (CRP) land in southwestern Iowa near Corning in the summers of 1991, 1992, 1993, 1994, and 1995. This report summarizes the 1995 data and compares them to results from the four previous years. The systems, a 13-paddock intensive-rotational grazing system and a 4-paddock more traditional rotation, both established in 1991, are aimed at showing economically sustainable grass alternatives for steeply sloping (9-14% slope), highly erodible land (HEL) once the 10-year CRP ends. In a 147-day grazing season in 1995, nursing crossbred calves with no creep gained 2.36 pounds and 2.38 pounds per day on the 13- and 4-paddock systems, respectively. The rotations were stocked at 1.65 acres per cow-calf pair on the 13-paddock system and 1.72 acres per pair on the 4-paddock system. This produced 210.2 pounds of calf gain per acre on the 13-paddock system and 203.2 pounds of calf gain per acre on the 4- paddock system.. Similar calves gained 2.37 pounds and 2.50 pounds per day for 155 days, yielding a total gain per acre of 222.7 pounds on the 13-paddock system and 224.9 pounds on the 4-paddock system in 1994. Results for 1992 remain the highest from both systems in the five years of grazing, with calf gain per head per day at 2.45 for 155 days netting 241.9 pounds per acre on the 13- paddock system and calf gain per head per day at 2.38 for 154 days on the 4-paddock system yielding 263.6 pounds per acre. Cows maintained both their weight and condition scores in both systems again in 1995. A third system, the 18-paddock intensive-rotational grazing system, was stocked with stocker steers in 1995, and the results are reported in a second article in the 1996 ISU Beef Research Report entitled “Intensive- Rotational Grazing Steers on Highly Erodible Land at the Adams County CRP Project.” Concerning grazing management, paddocks were grazed four, five, or six times in the 13-paddock intensive- rotational grazing system during the 147-day grazing season of 1995. This number of times grazed per paddock was nearly equal to times grazed per paddock in 1994. However, several paddocks were subdivided temporarily to equalize paddock size and increase grazing uniformity. This increased the total number of cattle moves in the 13-paddock system from 78 in 1994 to 109 in 1995. The average length of stay on each paddock or subdivision of a paddock per grazing time was 1 to 2.2 days. This was less than in any of the other four grazing years in this project. The principle of not grazing more than half the standing forage during any one grazing period was closely followed in 1995. All paddocks in the 13-paddock system were also rested approximately the recommended 30 days between each grazing cycle in 1995.

Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Triality, periodicity and stability of SO(8) gauged supergravity

While electromagnetic duality is a symmetry of many supergravity theories, this is not the case for the N = 8 gauged theory. It was recently shown that this rotation leads to a one-parameter family of SO(8) supergravities. It is an open question what the period of this parameter is. This issue is investigated in the SO(4) invariant sectors of the theory. We classify such critical points and find a novel branch of non-supersymmetric and unstable solutions, whose embedding is related via triality to the two known ones. Secondly, we show that the three branches of solutions lead to a π/4 periodicity of the vacuum structure. The general interrelations between triality and periodicity are discussed. Finally, we comment on the connection to other gauge groups as well as the possibility to achieve (non-)perturbative stability around AdS/Mkw/dS transitions.

The SU(3)-invariant sector of new maximal supergravity

We investigate the SU(3)-invariant sector of the one-parameter family of SO(8) gauged maximal supergravities that has been recently discovered. To this end, we construct the N=2 truncation of this theory and analyse its full vacuum structure. The number of critical point is doubled and includes new N=0 and N=1 branches. We numerically exhibit the parameter dependence of the location and cosmological constant of all extrema. Moreover, we provide their analytic expressions for cases of special interest. Finally, while the mass spectra are found to be parameter independent in most cases, we show that the novel non-supersymmetric branch with SU(3) invariance provides the first counterexample to this.