Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

Monte Carlo approaches to nonlinear optimal control

This paper explores the use of Monte Carlo techniques in deterministic nonlinear optimal control. Inter-dimensional population Markov Chain Monte Carlo (MCMC) techniques are proposed to solve the nonlinear optimal control problem. The linear quadratic and Acrobot problems are studied to demonstrate the successful application of the relevant techniques.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.

Chromosomal aberrations induced by C-12(6+) ions and Co-60 gamma-rays in mouse immature oocytes

The ovaries of Kun-Ming strain mice (3 weeks) were irradiated with different doses of C-12(6+) ion or Co-60 gamma-ray. Chromosomal aberrations were analyzed in metaphase II oocytes at 7 weeks after irradiation. The relative biological effectiveness (RBE) of C C-12(6+) ion was calculated with respect to Co-60 gamma-ray for the induction of chromosornal aberrations. The C-12(6+) ion and Co-60 gamma-ray dose-response relationships for chromosomal aberrations were plotted by linear quadratic models. The data showed that there was a dose-related increase in frequency of chromosomal aberrations in all the treated groups compared to controls. The RBE values for C-12(6+) ions relative to (CO)-C-60 gamma-rays were 2.49, 2.29, 1.57, 1.42 or 1.32 for the doses of 0.5, 1.0, 2.07 4.0 or 6.0 Gy, respectively. Moreover, a different distribution of the various types of aberrations has been found for C-12(6+) ion and Co-60 gamma-ray irradiations. The dose-response relationships for C-12(6+) ion and (CO)-C-60 gamma-ray exhibited positive correlations. The results from the present study may be helpful for assessing genetic damage following exposure of immature oocytes to ionizing radiation.

Biodosimetry estimate for high-LET irradiation

The purpose of this paper is to prepare for an easy and reliable biodosimeter protocol for radiation accidents involving high-linear energy transfer (LET) exposure. Human peripheral blood lymphocytes were irradiated using carbon ions (LET: 34.6 keV mu m(-1)), and the chromosome aberrations induced were analyzed using both a conventional colcemid block method and a calyculin A induced premature chromosome condensation (PCC) method. At a lower dose range (0-4 Gy), the measured dicentric (dics) and centric ring chromosomes (cRings) provided reasonable dose information. At higher doses (8 Gy), however, the frequency of dics and cRings was not suitable for dose estimation. Instead, we found that the number of Giemsa-stained drug-induced G2 prematurely condensed chromosomes (G2-PCC) can be used for dose estimation, since the total chromosome number (including fragments) was linearly correlated with radiation dose (r = 0.99). The ratio of the longest and the shortest chromosome length of the drug-induced G2-PCCs increased with radiation dose in a linear-quadratic manner (r = 0.96), which indicates that this ratio can also be used to estimate radiation doses. Obviously, it is easier to establish the dose response curve using the PCC technique than using the conventional metaphase chromosome method. It is assumed that combining the ratio of the longest and the shortest chromosome length with analysis of the total chromosome number might be a valuable tool for rapid and precise dose estimation for victims of radiation accidents.

A correlation between radiation sensitivity and initial chromatid breaks in cancer cell lines revealed by Calyculin A-induced premature condensation

Three human malignancy cell lines were irradiated with Co-60 gamma-rays. Initial chromatid breaks were measured by using the chemically induced premature chromosome condensation technique. Survival curves of cells exposed to gamma rays was linear-quadratic while the efficiency of Calyculin A in inducing PCC of G(2) PCC was about five times more than G(1) PCC. A dose-dependent increase in radiation-induced chromatid/isochromatid breaks was observed in G(1) and G(2) phase PCC and a nearly positive linear correlation was found between cell survival and chromatin breaks. This study implies that low LET radiation-induced chromatid/isochromatid breaks can potentially be used to predict the radiosensitivity of tumor cells either in in vitro experimentation or in in vivo clinical radiotherapy.

Comparison of clonogenic assay with premature chromosome condensation assay in prediction of human cell radiosensitivity

Aim: To determine whether the number of non-rejoining G2-chromatid breaks can predict the radiosensitivity of human cell lines. Methods: Cell lines of human ovary carcinoma cells (HO8910), human hepatoma cells (HepG2) and liver cells (L02) were irradiated with a range of doses and assessed both of cell survival and non-rejoining G2-chromatid breaks at 24 h after irradiation. Cell survival was documented by a colony assay. Non-rejoining G2-chromatid breaks were measured by counting the number of non-rejoining G2 chromatid breaks at 24 h after irradiation, detected by the prematurely chromosome condensed (PCC) technique. Results: A linear-quadratic survival curve was observed in three cell lines, and HepG2 was the most sensitive to gamma-radiation. A dose-dependent linear increase was observed in radiation-induced non-rejoining G2-PCC breaks measured at 24 h after irradiation in all cell lines, and HepG2 was the most susceptible to induction of non-rejoining G2-PCC breaks. A close correlation was found between the clonogenic radiosensitivity and the radiation-induced non-rejoining G2-PCC breaks (r=0.923). Furthermore, survival-aberration correlations for two or more than two doses lever were also significant. Conclusion: The number of non-rejoining G2 PCC breaks holds considerable promise for predicting the radiosensitivity of normal and tumor cells when two or more than two doses lever is tested.

Low-dose studies of bystander cell killing with targeted soft X rays

The Gray Cancer Institute ultrasoft X-ray microprobe was used to quantify the bystander response of individual V79 cells exposed to a focused carbon K-shell (278 eV) X-ray beam. The ultrasoft X-ray microprobe is designed to precisely assess the biological response of individual cells irradiated in vitro with a very fine beam of low-energy photons. Characteristic C-K X rays are generated by a focused beam of 10 keV electrons striking a graphite target. Circular diffraction gratings (i.e. zone plates) are then employed to focus the X-ray beam into a spot with a radius of 0.25 mum at the sample position. Using this microbeam technology, the correlation between the irradiated cells and their nonirradiated neighbors can be examined critically. The survival response of V79 cells irradiated with a C-K X-ray beam was measured in the 0-2-Gy dose range. The response when all cells were irradiated was compared to that obtained when only a single cell was exposed. The cell survival data exhibit a linear-quadratic response when all cells were targeted (with evidence for hyper-sensitivity at low doses). When only a single cell was targeted within the population, 10% cell killing was measured. In contrast to the binary bystander behavior reported by many other investigations, the effect detected was initially dependent on dose (200 mGy). In the low-dose region (

The design of a navigation guidance and control system for an unmanned surface vehicle for environmental monitoring

Maintaining the ecosystem is one of the main concerns in this modern age. With the fear of ever-increasing global warming, the UK is one of the key players to participate actively in taking measures to slow down at least its phenomenal rate. As an ingredient to this process, the Springer vehicle was designed and developed for environmental monitoring and pollutant tracking. This special issue paper highlighted the Springer hardware and software architecture including various navigational sensors, a speed controller, and an environmental monitoring unit. In addition, details regarding the modelling of the vessel were outlined based mainly on experimental data. The formulation of a fault tolerant multi-sensor data fusion technique was also presented. Moreover, control strategy based on a linear quadratic Gaussian controller was developed and simulated on the Springer model.
Gaussian controller is developed and simulated on the Springer model.

Out-of-field cell survival following exposure to intensity-modulated radiation fields

PURPOSE:
To determine the in-field and out-of-field cell survival of cells irradiated with either primary field or scattered radiation in the presence and absence of intercellular communication.
METHODS AND MATERIALS:
Cell survival was determined by clonogenic assay in human prostate cancer (DU145) and primary fibroblast (AGO1552) cells following exposure to different field configurations delivered using a 6-MV photon beam produced with a Varian linear accelerator.
RESULTS:
Nonuniform dose distributions were delivered using a multileaf collimator (MLC) in which half of the cell population was shielded. Clonogenic survival in the shielded region was significantly lower than that predicted from the linear quadratic model. In both cell lines, the out-of-field responses appeared to saturate at 40%-50% survival at a scattered dose of 0.70 Gy in DU-145 cells and 0.24 Gy in AGO1522 cells. There was an approximately eightfold difference in the initial slopes of the out-of-field response compared with the a-component of the uniform field response. In contrast, cells in the exposed part of the field showed increased survival. These observations were abrogated by direct physical inhibition of cellular communication and by the addition of the inducible nitric oxide synthase inhibitor aminoguanidine known to inhibit intercellular bystander effects. Additional studies showed the proportion of cells irradiated and dose delivered to the shielded and exposed regions of the field to impact on response.
CONCLUSIONS:
These data demonstrate out-of-field effects as important determinants of cell survival following exposure to modulated irradiation fields with cellular communication between differentially irradiated cell populations playing an important role. Validation of these observations in additional cell models may facilitate the refinement of existing radiobiological models and the observations considered important determinants of cell survival.

An Autopilot Based on a Local Control Network Design for an Unmanned Surface Vehicle

Over recent years, a number of marine autopilots designed using linear techniques have underperformed owing to their inability to cope with nonlinear vessel dynamics. To this end, a new design framework for the development of nonlinear autopilots is proposed herein. Local control networks (LCNs) can be used in the design of nonlinear control systems. In this paper, a LCN approach is taken in the design of a nonlinear autopilot for controlling the nonlinear yaw dynamics of an unmanned surface vehicle known as Springer. It is considered the approach is the first of its kind to be used in marine control systems design. Simulation results are presented and the performance of the nonlinear autopilot is compared with that of an existing Springer linear quadratic Gaussian (LQG) autopilot using standard system performance criteria. From the results it can be concluded the LCN autopilot out performed that based on LQG techniques in terms of the selected criteria. Also it provided more energy saving control strategies and would thereby increase operational duration times for the vehicle during real-time missions.

Cell survival responses after exposure to modulated radiation fields.

In the present study survival responses were determined in cells with differing radiosensitivity, specifically primary fibroblast (AG0-1522B), human breast cancer (MDA-MB-231), human prostate cancer (DU-145) and human glioma (T98G) cells, after exposure to modulated radiation fields delivered by shielding 50% of the tissue culture flask. A significant decrease (P < 0.05) in cell survival was observed in the shielded area, outside the primary treatment field (out-of-field), that was lower than predicted when compared to uniform exposures fitted to the linear-quadratic model. Cellular radiosensitivity was demonstrated to be an important factor in the level of response for both the in- and out-of-field regions. These responses were shown to be dependent on secretion-mediated intercellular communication, because inhibition of cellular secreted factors between the in- and out-of-field regions abrogated the response. Out-of-field cell survival was shown to increase after pretreatment of cells with agents known to inhibit factors involved in mediating radiation-induced bystander signaling (aminoguanidine, DMSO or cPTIO). These data illustrate a significant decrease in survival out-of-field, dependent upon intercellular communication, in several cell lines with varying radiosensitivity after exposure to a modulated radiation field. This study provides further evidence for the importance of intercellular signaling in modulated exposures, where dose gradients are present, and may inform the refinement of established radiobiological models to facilitate the optimization of advanced radiotherapy treatment plans.

DNA damage induction in dry and hydrated DNA by synchrotron radiation

Radiation biophysics has sought to understand at a molecular level, the mechanisms through which ionizing radiations damage DNA, and other molecules within living cells. The complexity of lesions produced in the DNA by ionizing radiations is thought to depend on the amount of energy deposited at the site of each lesion. To study the relationship between the energy deposited and the damage produced, we have developed novel techniques for irradiating dry prasmid DNA, partially re-hydrated DNA and DNA in solution using monochromatic vacuum-UV synchrotron radiation. We have used photons in the energy range 7-150 eV, corresponding to the range of energies typically involved in the efficient production of DNA single-strand (SSB), and double-strand breaks (DSB) by ionizing radiation. The data show that both types of breaks are produced at all energies investigated (with, or without water present). Also, the energy dependence for DSB induction follows a similar trend to SSB induction but at a 20-30-fold reduced incidence, suggesting a common precursor for both types of damage. Preliminary studies where DNA has been irradiated in solution indicate a change in the shape of the dose-effect curve (from linear, to linear-quadratic for double-strand break induction) and a large increase in sensitivity due to the presence of water.

Recognition of O6MeG lesions by MGMT and mismatch repair proficiency may be a prerequisite for low-dose radiation hypersensitivity

Low-dose hyper-radiosensitivity (HRS) is the phenomenon whereby cells exposed to radiation doses of less than approximately 0.5 Gy exhibit increased cell killing relative to that predicted from back-extrapolating high-dose survival data using a linear-quadratic model. While the exact mechanism remains to be elucidated, the involvement of several molecular repair pathways has been documented. These processes in turn are also associated with the response of cells to O6-methylguanine (O6MeG) lesions. We propose a model in which the level of low-dose cell killing is determined by the efficiency of both pre-replicative repair by the DNA repair enzyme O6-methylguanine methyltransferase (MGMT) and post-replicative repair by the DNA mismatch repair (MMR) system. We therefore hypothesized that the response of cells to low doses of radiation is dependent on the expression status of MGMT and MMR proteins. MMR (MSH2, MSH6, MLH1, PMS1, PMS2) and MGMT protein expression signatures were determined in a panel of normal (PWR1E, RWPE1) and malignant (22RV1, DU145, PC3) prostate cell lines and correlated with clonogenic survival and cell cycle analysis. PC3 and RWPE1 cells (HRS positive) were associated with MGMT and MMR proficiency, whereas HRS negative cell lines lacked expression of at least one (MGMT or MMR) protein. MGMT inactivation had no significant effect on cell survival. These results indicate a possible role for MMR-dependent processing of damage produced by low doses of radiation.