Off-lattice random walks with excluded volume: a new method of generation, proof of ergodicity and numerical results

The development of new methods for generating pulsed electromagnetic microwave radiation is currently an actively developing area of research. Schemes for microwave radiation generation with optical pumping are of great interest. In this paper we propose and experimentally demonstrate principally new method for photonic generation of microwave electromagnetic radiation. This method is based on the use of radiation of charged submicron particles oscillating at their own acoustic frequency. Laser radiation of the optical range implements an effective buildup of acoustic vibrations of submicron particles forming the system under study, according to the Raman mechanism.

Orbital Angular Momentum (OAM) has drawn great attention of worldwide academia in the recent years. It has been intensively applied in the domains of optics. Recent studies imply that OAM vortex wave can be used in radio not only limited to optics. Then, the application of OAM in radio has gradually become a research hotspot, and developing effective antennas to produce OAM beams is one of the key issues. To date, there are several methods to generate OAM beams, such as spiral phase plate, holographic diffraction gratings, spiral reflectors, and antenna arrays. Among them, the first two methods come from the optics and mainly going to be used in high frequency like millimeter wave. The latter two types mainly targets the low frequency. However, the spiral reflectors in many cases, due to its specifically curved surface, is difficult to manufacture. On the other hand, the array antenna, when equipped with controllable phase shifters, can achieve different functionalities electronically, but generally becomes very expensive due to its complicated beam-former and many high-cost amplifier modules. Here, we present a new method for the generation of an electromagnetic vortex wave by reflective metasurface in radio frequency. It can easily avoided transmission loss, and has the flexibility in phase control. The proposed method paves a new way to generate the OAM vortex waves for radio and microwave wireless communication applications.

As a result of a pressing need for function generators, a new method of function generation has been developed. The underlying principle of this function generator is the application of ordinary pulse techniques in such a way as to produce a function. The simplicity of design, the high accuracy attainable, the simple type of construction are the outstanding features of this general-purpose function generator. In order to compare this new type of function generator with those presently being used, three important types are discussed. These generators are of the general-purpose, electric and photoelectric types; other comparable electromechanical types are excluded. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>

We have performed computer simulations of closed polymer chains with allowance for the excluded volume effects within the framework of the free-joint model. The probability of knot formation, the linking probability of a pair of chains and the variance in the writhing number proved to be significantly affected by the excluded volume effects. This is true even for DNA with completely screened charges for which the b/d ratio (where b is the Kuhn statistical length and d is the diameter of the double helix) is as large as 50. Allowance for the electrostatic repulsion (change of the DNA effective diameter d) further increases the effects. The most dramatic dependence on d is found for the probability of knot formation. The data on the dependence of the variance of writhing, mean value of (WR)2, on d indicate that the DNA superhelix energy should be significantly ionic strength-dependent. Special calculations have shown that the free-joint model underestimates the mean value of (Wr)2 value by about 20% as compared with the wormlike model.

By means of Monte Carlo simulation, linear (F=2) and star-branched tetrahedral lattice chains with F=3–12 arms of length n=480 connected to a hard core consisting of MIN(5,F+1) segments (the total number of segments thus ranging from 963 to 5765) were produced for athermal and theta conditions. Nonreversal random walks (random walks without backfolding bonds) were generated as a reference. Several quantities (asphericity factor δ*, prolateness factor S*, and shape factors sfi*) characteristic of the instantaneous shape of molecules—being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia—were computed. The probability distributions of these quantities were calculated and their interdependence as well as their correlation with quantities characteristic of the size of configurations was analyzed. Shape and size of star-branched chains for athermal as well as for theta conditions are highly correlated as earlier found for linear chains and random walk stars. The broadness of distribution functions decreases with increasing number of arms, but remains appreciably for F=12, the system with the largest functionality evaluated.

Computerized generation of surfaces with optimal approximation to ideal surfaces

A new method of generation and adaptation of multi-axis machines ultrasonic machining paths, geometric change in gross machining is proposed in this paper. Currently, these are in most machining time are done manually by highly trained operators. The proposed method starts with a first step of association using an Iterative Closest Point "ICP" algorithm. In the second step, a deforming toolpath is given. To validate the theoretical developments, experimental tests were carried out for a uni-compartmental femoral knee component.

Monte Carlo simulations of self-avoiding random walks surrounded by aligned rods on a square lattice and a simple cubic lattice were performed to address the topological constraints involved for dilute solutions of flexible polymers in a highly oriented nematic solvent. The nematic constraint exerted by the solvent is modelled by requiring that the distance between nearest neighbour chain segments in the direction of the director of the nematic solvent is such that a discrete number of rods, representing the perfectly ordered nematic solvent, fits exactly in between. Rod lengths of one or two lattice spacings are used. In this case interesting scaling behaviour for the radius of gyration and the end-to-end distance is found. Perpendicular to the director the coil behaves as a two- (or one- in the case of a square lattice) dimensional self-avoiding walk, whereas parallel to the director it behaves as a random walk. The conformations have a disk-like shape with the radius of gyration perpendicular to the director being considerably larger than the parallel component. These simulations address only one aspect of flexible polymers in nematic solvents. In reality the presence of the coil also reduces the entropy of the solvent which has exactly the opposite effect on the shape of the polymer coil.

The generation of droplet is indispensable for micro-fluidic device. A new method for generation of droplet was proposed. An interdigital transducer and reflector were fabricated on a 128°yx-LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> substrate. A PDMS micro-channel with back taper shape was used to connect a syringe and a needle with sub-micron inside diameter, which was supported by arc PDMS. The tip of the needle was above the piezoelectric substrate with small distance. Fluid was aggregated at the tip of the needle due to the syringe pump. As soon as the fluid was large enough and contacted to the piezoelectric substrate, the fluid was driven by surface acoustic wave and finished the generation of one droplet. Red dye solution was used to generation experiment of droplet. Results show that the volume of generated droplet is decided on the needle radius, the gap between the needle and the piezoelectric substrate and RF signal power. The method of droplet generation is useful for lab-on-a-piezoelectric-substrate for biochemical analysis.

In all systems simulation, random variates are considered as a main factor and based of simulation heart. Actually, randomization is inducted by random variates in the simulation. Due to the importance of such a problem, a new method for generation of random variates from continuous distributions is presented in this paper. The proposed algorithm, called uniform fractional part (UFP) is simpler and more efficient compared with other methods of random variates generation. Despite useful consequences, this algorithm has several shortcomings such as 1) being approximate, 2) not accessibility of the inverse of cumulative density function (CDF) for all distributions in order to determine the cut-off points and 3) truncating the tails of infinite distributions, which all of the aforementioned shortcomings reduce the precision and speed of the algorithm. The main goal of this research is proposing the improved version of this algorithm (IUFP) through recognizing its deficiencies.

This monograph focuses on random walks in the quarter-plane. Such random walks are frequently used to model queueing systems and the invariant measure of a random walk is of major importance in studying the performance of these systems. In special cases the invariant measure of a random walk can be expressed as a geometric product-form and performance measures can readily be obtained. In general, however, no tractable closed-form expressions are available for the invariant measure and exact performance measures are not readily obtained. The aim of this monograph is two-fold. On one hand we consider measures that are a sum of geometric terms. We characterize the random walks in the quarter-plane of which the invariant measure is of this form. This extends the class of random walks for which tractable closed-form results can be obtained. On the other hand we develop approximation schemes that provide analytical upper and lower bounds on performance for the case that no tractable closed-form expressions for the invariant measure are available. It is shown that the necessary conditions that are required to have an invariant measure which is a sum of geometric terms are as follows: Each geometric term must individually satisfy the balance equations in the interior of the state space and the geometric terms in an invariant measure must have a pairwise-coupled structure. Moreover, at least one of the coecients in the linear combination must be negative. When the invariant measure of the random walk is a sum of innitely many geometric terms, it is also required that the random walk does not have transitions to the North, Northeast or East in the interior of the state space. Based on the necessary conditions described above, we develop an algorithm which determines whether the invariant measure of a given random walk is a sum of geometric terms. For the case that the invariant measure of this random walk is not a sum of geometric terms, we have developed an approximation scheme to find upper and lower bounds for the performance measures. This approximation scheme is based on a Markov reward approach to error bounds. The bounds determined by our approximation scheme are established in terms of a perturbed random walk of which the invariant measure is a sum of geometric terms. Numerical results reveal that using a perturbed random walk of which the invariant measure is a sum of multiple geometric terms may lead to better bounds than using perturbed random walks of which the invariant measure is of product-form. Finally, we have also extended this approximation scheme to two-dimensional finite random walks.

Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to the size variations, polyelectrolytes of fixed chain length are classified into three categories: (1) flexible chain, for which the variation shows a curve similar to a tilted L, (2) semiflexible chain, whose curve resembles U, and (3) rigid chain, for which the curve is a straight line. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. In a low salt region, a flexible polyelectrolyte extends more significantly than a semiflexible chain, in reference of the size of their uncharged counterparts, and in a high salt region, regardless of chain stiffness, a chain attains a dimension comparable to that of its neutral polymer. The chain stiffness influences both the local and the global chain structures. A flexible chain exhibits a zigzagged local structure in the presence of salt ions, and the condensed structure is a disordered, random globule. A semiflexible chain is locally smooth, and the condensed structure is orderly packed, taking a form such as hairpin or toroid. Moreover, the chain stiffness can also affect the nature of the coil-globule transition. The transition occurred in a discrete manner for semiflexible chain, whereas it occurred in a continuous way for flexible chain. This discrete feature happened not only at low salt concentration when a semiflexible chain collapsed but also at high salt concentration when the collapsed chain is reexpanded. At the end, the effects of chain stiffness and salt concentration on the conformation of single polyelectrolytes are summarized in a schematic state diagram.

A mean-field, lattice model of polymer solutions is developed which accounts for both excluded-volume and attractive interactions. A screening length, xs, is defined such that for configurations that have a gyration radius S that is larger than xs, the intramolecular interactions are partially screened by intermolecular interactions. If the configuration is smaller than xs, intramolecular interactions are not screened. Thus, xs is a function of polymer concentration, c, and molecular weight, M. Three separate regions for solutions are found, based on the size of xs: 1) dilute solutions (c c**) for which xs is smaller than the average size of an ideal chain, so that the chains overlap strongly; and 3) semi-dilute solutions (c*<c<c**) for which xs is comparable to the sizes of the chains and so there is an intermediate degree of overlap. A unique method of calcula...

Mean-square radius of gyration and hydrodynamic radius for topological polymers evaluated through the quaternionic algorithm

Correlation between shape and size of linear polymer chains