Publications by Colleges and Departments (MSU - Bozeman)
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Item Radiometry and the Friis transmission equation(American Association of Physics Teachers, 2013) Shaw, JosephTo more effectively tailor courses involving antennas, wireless communications, optics, and applied electromagnetics to a mixed audience of engineering and physics students, the Friis transmission equation—which quantifies the power received in a free-space communication link—is developed from principles of optical radiometry and scalar diffraction. This approach places more emphasis on the physics and conceptual understanding of the Friis equation than is provided by the traditional derivation based on antenna impedance. Specifically, it shows that the wavelength-squared dependence can be attributed to diffraction at the antenna aperture and illustrates the important difference between the throughput (product of area and solid angle) of a single antenna or telescope and the throughput of a transmitter-receiver pair.Item Model-Based Closed-Loop Control of the Hydraulic Fracturing Process(2015-02) Gu, Qiuying; Hoo, Karlene A.Hydraulic fracturing is a technique for enhancing the extraction of oil and gas from deep underground sources. Two important goals during this process are to achieve a final fracture with a predefined geometry and to have a proper distribution of proppant material within the fracture to keep the fracture walls open and allow oil and gas to flow to the surface. The hydraulic fracturing system contains limited real-time measurements of the actual fracture conditions largely due to the remote subterranean location where the fracture propagates. The fracturing process is characterized by multiphase transport, proppant settling, and coupling of fluid and fracture growth mechanics, all occurring within a time-varying spatial domain. These features present a challenge for the implementation of online feedback control of the fracture growth and proppant placement, and there are very few accounts of attempting this goal in the open literature. To address these issues, the current work proposes a control strategy that allows for closed-loop model-based control of the hydraulic fracturing process. Previous work introduced a dynamic fracture model capable of describing the fracture propagation, fluid and particle transport, proppant bank formation, and fracture closure processes necessary to determine the fracture state evolution and predict the fracture’s final performance. The QDMC (quadratic-dynamic matrix control) form of model-based control is studied. A particle filter provides a means for effective state estimation due to limited real-time measurements. Controlling the fracture geometry and proppant distribution within a hydraulic fracture is a novel application for real-time model-based control. Results of a numerical study are provided to demonstrate the performance of the closed-loop system.Item Correcting for focal-plane-array temperature dependence in microbolometer infrared cameras lacking thermal stabilization(2013-01) Nugent, Paul W.; Shaw, Joseph A.; Pust, Nathan J.Advances in microbolometer detectors have led to the development of infrared cameras that operate without active temperature stabilization. The response of these cameras varies with the temperature of the camera’s focal plane array (FPA). This paper describes a method for stabilizing the camera’s response through software processing. This stabilization is based on the difference between the camera’s response at a measured temperature and at a reference temperature. This paper presents the mathematical basis for such a correction and demonstrates the resulting accuracy when applied to a commercially available long-wave infrared camera. The stabilized camera was then radiometrically calibrated so that the digital response from the camera could be related to the radiance or temperature of objects in the scene. For FPA temperature deviations within ±7.2°C changing by 0.5°C/min, this method produced a camera calibration with spatial-temporal rms variability of 0.21°C, yielding a total calibration uncertainty of 0.38°C limited primarily by the 0.32°C uncertainty in the blackbody source emissivity and temperature.Item Search for tricritical point in KH2PO4 at high pressure. I. Static dielectric behavior near critical point at zero pressure(1977-01) Western, Arthur B.; Baker, A. G.; Pollina, R. J.; Schmidt, V. HugoThe proposed tricritical point in KDP occurs if the critical field, Ecr, can be brought to zero by applying pressure. The Landau equation of state E = A0(T - T0)P + BP3 + CP5 gives straight-line “isopols” in the T-E plane. We obtain values for A0, B and C and thus Ecr by observing such isopols. We find A0 = 4.3 × 10-3; B = -2.35 × 10-11 C = 5.91 × 10-19 cgs esu for the crystal studied at ambient pressure. These values lead to Ecr = 232 V/cm and δPspon (Tc) = 1.82 C/cm2. High pressure results are imminent.Item Tricritical point and tricritical exponent δ in KH2PO4(1978-01) Schmidt, V. Hugo; Western, Arthur B.; Baker, A. G.; Bacon, Charles R.Static dielectric results for a KH2PO4 crystal at pressures of 0, 2, and 2. 4 kbar are analyzed in terms of a Landau free energy expansion using the “isopol” technique. The measured exponent δ at 2. 4 kbar is consistent with the mean-field tricritical value of 5. This result and the Landau parameter values indicate a tricritical point near 2. 4 kbar.Item A Novel Method for Curvefitting the Stretched Exponential Function to Experimental Data(2013-12) June, Ronald K.; Cunningham, J. P.; Fyhrie, D. P.The stretched exponential function has many applications in modeling numerous types of experimental relaxation data. However, problems arise when using standard algorithms to fit this function: we have observed that different initializations result in distinct fitted parameters. To avoid this problem, we developed a novel algorithm for fitting the stretched exponential model to relaxation data. This method is advantageous both because it requires only a single adjustable parameter and because it does not require initialization in the solution space. We tested this method on simulated data and experimental stress-relaxation data from bone and cartilage and found favorable results compared to a commonly-used Quasi-Newton method. For the simulated data, strong correlations were found between the simulated and fitted parameters suggesting that this method can accurately determine stretched exponential parameters. When this method was tested on experimental data, high quality fits were observed for both bone and cartilage stress-relaxation data that were significantly better than those determined with the Quasi-Newton algorithm.Item Exact solution in the discrete case for solitons propagating in a chain of harmonically coupled particles lying in double-minimum potential wells(1979-12) Schmidt, V. HugoSolitons of the form xn=x0tanh(ωt−kna) can propagate in a chain of harmonically coupled particles in the discrete case if the potential −1/2Axn^2+1/4Bxn^4 giving such solitions in the continuum limit is suitably modified. This modified potential is expressible in closed form, and its shape is a function of ω and k. For large ω the maximum at xn=0 becomes a minimum, giving a triple-minimum potential. Potential shapes and particle positions are illustrated for various (ω,k) combinations. The total energy and its kinetic, potential, and spring energy constituents are also expressible in closed form. In the continuum limit the total energy has the form E=(m0cS^2)/(1−v^2/cS^2)^1/2, where m0 is the soliton effective mass, v is the soliton speed, and cS is the speed of sound in the mass-spring chain.Item Semiclassical theory of proton transport in ice(1967-04) Kim, Dong-Yun; Schmidt, V. HugoA method is described for calculating proton or other ion mobility which is applicable if mobility is limited by lattice scattering rather than by barrier jumping. The Boltzmann transport equation is used, with the collision term calculated from the electrostatic interactions between the mobile ion and the vibrating lattice. In particular the proton mobility in ice is calculated. The lattice vibrations are approximated by a Debye spectrum for translational vibrations of water molecules, plus an Einstein spectrum for modes in which protons vibrate almost as independent particles. Scattering by phonons somewhat below the Debye cutoff frequency is of the greatest importance in determining the mobility, and the proton modes have negligible effect. The calculated mobility agrees reasonably well with the experimental value.Item AC Susceptibility of Biased One-Dimensional Stochastic Ising Model.(1971-06) Schmidt, V. HugoThe ac susceptibility for the one‐dimensional Ising model is obtained for arbitrary coupling strength in the presence of a dc bias field strong enough to align most of the dipoles in one direction. The dipole flip probability is assumed proportional to the Boltzmann factor corresponding to half the energy change resulting from the flip. The general expression for ac susceptibility is analyzed in three limiting cases: weak coupling with strong bias, strong coupling with strong bias, and strong coupling with weak bias. In the latter case, relatively long chains of anti‐aligned dipoles exist and give rise to large susceptibility.Item Quantifying the effects of the division of labor in metabolic pathways(Elsevier, 2014-11) Harvey, Emily; Heys, Jeffrey J.; Gedeon, TomasDivision of labor is commonly observed in nature. There are several theories that suggest diversification in a microbial community may enhance stability and robustness, decrease concentration of inhibitory intermediates, and increase efficiency. Theoretical studies to date have focused on proving when the stable co-existence of multiple strains occurs, but have not investigated the productivity or biomass production of these systems when compared to a single ‘super microbe’ which has the same metabolic capacity. In this work we prove that if there is no change in the growth kinetics or yield of the metabolic pathways when the metabolism is specialised into two separate microbes, the biomass (and productivity) of a binary consortia system is always less than that of the equivalent monoculture. Using a specific example of Escherichia coli growing on a glucose substrate, we find that increasing the growth rates or substrate affinities of the pathways is not sufficient to explain the experimentally observed productivity increase in a community. An increase in pathway efficiency (yield) in specialised organisms provides the best explanation of the observed increase in productivity.