An efficient perturbation theory of density matrix renormalization group

Density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. In this work, we develop a perturbation theory of DMRG (PT-DMRG) to largely increase its accuracy in an extremely simple and efficient way. By using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions $\left\lbrace | \psi_i \rangle \right\rbrace$ is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cut-off are used to define such perturbation terms. The perturbed Hamiltonian is then defined as $\tilde{H}_{ij}= \langle \psi_i | \hat{H} | \psi_j \rangle$; its ground state permits to calculate physical observables with a considerably improved accuracy as compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of DMRG is shown to be improved $\rm O(10)$ times. Furthermore, for moderate length $L$ the errors of DMRG and PT-DMRG both scale linearly with $L^{-1}$. The linear relation between the dimension cut-off of DMRG and that of PT-DMRG with the same precision shows a considerable improvement of efficiency, especially for large dimension cut-off's. In thermodynamic limit we show that the errors of PT-DMRG scale with $\sqrt{L^{-1}}$. Our work suggests an effective way to define the tangent space of the ground state MPS, which may shed lights on the properties beyond the ground state. Such second-order PT-DMRG can be readily generalized to higher orders, as well as applied to the models in higher dimensions

Photochemical reactions of cyanoacetylene and dicyanoacetylene: Possible processes in Titan's atmosphere

Titan has an atmosphere which is subject to dramatic chemical evolution due mainly to the dramatic effect of the UV flux from the Sun. The energetic solar photons and other particles are converting the methane-nitrogen atmosphere into the unsaturated carbon compounds observed by the Voyager probes. These same solar photons are also converting some of these unsaturated reaction products into the aerosols observed in the atmosphere which obscure the view of the surface of Titan. In particular, the photochemical reactions of cyanoacetylene, dicyanoacetylene, acetylene and ethylene may result in the formation of the higher hydrocarbons and polymers which result in the aerosols observed in Titan's atmosphere. Polymers are the principal reaction products formed by irradiation of cyanoacetylene and dicyanoacetylene. Irradiation of cyanoacetylene with 185 nm of light also yields 1,3,5-tricyanobenzene while irradiation at 254 nm yields 1,2,4-tricyanobenzene and tetracyano cyclooctatetraenes. Photolyses of mixtures of cyanoacetylene and acetylene yields mono- and di- cyanobenzenes. The 1-Cyanocyclobutene is formed from the photochemical addition of cyanoacetylene with ethylene. The photolysis of dicyanoacetylene with acetylene yields 2,3-dicyano-1,3-butadiene and 1,2-dicyanobenzene. Tetracyano cyclooctatetraene products were also observed in the photolysis of mixtures of dicyanoacetylene and acetylene with 254 nm light. The 1,2-Dicyano cyclobutene is obtained from the photolysis dicyanoacetylene and ethylene. Reaction mechanisms will be proposed to explain the observed photoproducts

Results of correlations for transition location on a clean-up glove installed on an F-14 aircraft and design studies for a laminar glove for the X-29 aircraft accounting for spanwise pressure gradient

Results of correlative and design studies for transition location, laminar and turbulent boundary-layer parameters, and wake drag for forward swept and aft swept wings are presented. These studies were performed with the use of an improved integral-type boundary-layer and transition-prediction methods. Theoretical predictions were compared with flight measurements at subsonic and transonic flow conditions for the variable aft swept wing F-14 aircraft for which experimental pressure distributions, transition locations, and turbulent boundary-layer velocity profiles were measured. Flight data were available at three spanwise stations for several values of sweep, freestream unit Reynolds number, Mach numbers, and lift coefficients. Theory/experiment correlations indicate excellent agreement for both transition location and turbulent boundary-layer parameters. The results of parametric studies performed during the design of a laminar glove for the forward swept wing X-29 aircraft are also presented. These studies include the effects of a spanwise pressure gradient on transition location and wake drag for several values of freestream Reynolds numbers at a freestream Mach number of 0.9

Molecular and mass spectroscopic analysis of isotopically labeled organic residues

Experimental studies aimed at understanding the evolution of complex organic molecules on interstellar grains were performed. The photolysis of frozen gas mixtures of various compositions containing H2O, CO, NH3, and CH4 was studied. These species were chosen because of their astrophysical importance as deducted from observational as well as theoretical studies of ice mantles on interstellar grains. These ultraviolet photolyzed ices were warmed up in order to produce refractory organic molecules like the ones formed in molecular clouds when the icy mantles are being irradiated and warmed up either by a nearby stellar source or impulsive heating. The laboratory studies give estimates of the efficiency of production of such organic material under interstellar conditions. It is shown that the gradual carbonization of organic mantles in the diffuse cloud phase leads to higher and higher visual absorptivity - yellow residues become brown in the laboratory. The obtained results can be applied to explaining the organic components of comets and their relevance to the origin of life

Dairy Cow Performance Associated with Two Contrasting Silage Feeding Systems

As a result of increasing labour costs, the lack of skilled labour, and the desire of many farmers to reduce their working hours, there is considerable interest in using simple feeding systems for dairy cows. A study was conducted to compare two silage feeding systems that differed in complexity

A Biomechanical Comparison of Proportional Electromyography Control to Biological Torque Control Using a Powered Hip Exoskeleton

BackgroundDespite a large increase in robotic exoskeleton research, there are few studies that have examined human performance with different control strategies on the same exoskeleton device. Direct comparison studies are needed to determine how users respond to different types of control. The purpose of this study was to compare user performance using a robotic hip exoskeleton with two different controllers: a controller that targeted a biological hip torque profile and a proportional myoelectric controller.MethodsWe tested both control approaches on 10 able-bodied subjects using a pneumatically powered hip exoskeleton. The state machine controller targeted a biological hip torque profile. The myoelectric controller used electromyography (EMG) of lower limb muscles to produce a proportional control signal for the hip exoskeleton. Each subject performed two 30-min exoskeleton walking trials (1.0 m/s) using each controller and a 10-min trial with the exoskeleton unpowered. During each trial, we measured subjects’ metabolic cost of walking, lower limb EMG profiles, and joint kinematics and kinetics (torques and powers) using a force treadmill and motion capture.ResultsCompared to unassisted walking in the exoskeleton, myoelectric control significantly reduced metabolic cost by 13% (p = 0.005) and biological hip torque control reduced metabolic cost by 7% (p = 0.261). Subjects reduced muscle activity relative to the unpowered condition for a greater number of lower limb muscles using myoelectric control compared to the biological hip torque control. More subjects subjectively preferred the myoelectric controller to the biological hip torque control.ConclusionMyoelectric control had more advantages (metabolic cost and muscle activity reduction) compared to a controller that targeted a biological torque profile for walking with a robotic hip exoskeleton. However, these results were obtained with a single exoskeleton device with specific control configurations while level walking at a single speed. Further testing on different exoskeleton hardware and with more varied experimental protocols, such as testing over multiple types of terrain, is needed to fully elucidate the potential benefits of myoelectric control for exoskeleton technology

The Effect of Inclusion of a Range of Supplementary Feeds on Herbage Intake, Total Dry Matter Intake and Substitution Rate in Grazing Dairy Cows

The milk production potential of dairy cows has increased substantially over the past two decades. This development presents new challenges for managing dairy cows during grazing, particularly where the objective is to maximise the proportion of energy in the diet derived from forage. The objective of the current study was to explore supplementation strategies to maintain high total forage intakes from grazed grass supplemented with alternative forage supplements in dairy cows during the grazing season. A second objective of the study was to examine the effect of supplement on substitution rate (SR) and milk yield response

Dynamical instabilities of Bose-Einstein condensates at the band-edge in one-dimensional optical lattices

We report on experiments that demonstrate dynamical instability in a Bose-Einstein condensate at the band-edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and perform numerical modeling of the experiments using both a mean-field and beyond mean-field approach. We compare our numerical results to the experimental data, and find that the Gross-Pitaevskii equation is not able to describe this experiment. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and thermalization that are observed in the laboratory, and we find good agreement with the experimental results.Comment: v2: Added several reference

Evaluating the marketing opportunities for shea nut and shea nut processed products in Uganda

This study was commissioned by USAID -Kampala to evaluate the economic and environmental prospects for the Shea sector of Uganda. Specifically the study aimed to evaluate the prospects for a range of Shea products for local, national and international markets. The output from the study being to provide options for improving the livelihoods of communities based in the Shea producing areas of Uganda and suggesting possible strategies to assist greater commercialisation of this novel, traditional product within an environmentally sustainable manner