Closed-form MSE and achievable rate for indirect learning DPD

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption, etc. Consequently, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations.     

Multiscale simulation of carbon nanotube devices

In recent years, the understanding and accurate simulation of carbon nanotube-based devices has become very challenging. Conventional simulation tools of microelectronics are necessary to envision the performance and use of nanotube transistors and circuits, but the models need to be refined to properly describe the full complexity of such novel type of devices at the nanoscale. Indeed, many issues such as contact resistance, low dimensional electrostatics and screening effects, as well as nanotube doping or functionalization, demand for more accurate quantum approaches. In this article, we review our recent progress on multiscale simulations which aim at bridging first principles calculations with compact modelling, including the comparison between semi-classical Monte Carlo and quantum transport approaches. To cite this article: C. Adessi et al., C. R. Physique 10 (2009).     

Accurate treatments of electrostatics for computer simulations of biological systems: A brief survey of developments and existing problems

Modern computer simulations of biological systems often involve an explicit treatment of the complex interactions among a large number of molecules. While it is straightforward to compute the short-ranged Van der Waals interaction in classical molecular dynamics simulations, it has been a long-lasting issue to develop accurate methods for the longranged Coulomb interaction. In this short review, we discuss three types of methodologies for the accurate treatment of electrostatics in simulations of explicit molecules: truncation-type methods, Ewald-type methods, and mean-field-type methods. Throughout the discussion, we brief the formulations and developments of these methods, emphasize the intrinsic connections among the three types of methods, and focus on the existing problems which are often associated with the boundary conditions of electrostatics. This brief survey is summarized with a short perspective on future trends along the method developments and applications in the field of biological simulations.     

Collective and single particle diffusion on surfaces

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These first three sections form an introduction to the field of surface diffusion. Section 4 contains subsections that discuss surface diffusion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on specific systems but rather on important issues concerning diffusion measurements or calculations. Examples include the influence of steps, diffusion in systems undergoing phase transitions, and the role of correlation and memory effects. Obviously, the choice of topics here reflects the interest and expertise of the authors and is by no means exhaustive. Nevertheless, these topics form a collection of issues that are under active investigation, with many important open questions remaining.     

Closed-form analysis for indirect learning digital pre-distorter for wideband wireless systems

Indirect learning architecture (ILA) for digital pre-distortion (DPD) is commonly used to linearize power amplifiers (PA). To the author’s best knowledge, most of the DPD results in the literature obtain the matrix form of the least-square solution in order to get the DPD coefficients numerically. There exists no explicit closed-form for these coefficients that can be used as plug-and-play in simulations, or used for further closed-form analysis of important measures such as signal-to-noise ratio (SNR) and mean square error (MSE), bit-error rate (BER), …etc. In this paper, we analyze the ILA-DPD system for general memory-polynomial PA models. We provide a closed-form solution for the DPD coefficients. We first present the analytical methodology for deriving the mathematical expressions for each DPD coefficient and then introduce an open-access code that generates the DPD coefficients in symbolic form that is used to mathematically model the DPD. We consider case studies for PA and show that the analytical DPD solution matches the Monte Carlo simulations. Moreover, we also provide a closed-form solution for the iterative adaptive ILA-DPD. Our analysis shows that in the case of a large training block length the non-iterative DPD achieves approximately the same performance as an iterative DPD with a shorter training block length. System impairments are also considered, e.g. the thermal noise and the quantization noise in analog–digital conversion (ADC). We derive the normalized mean square error (NMSE) for the transmit chain in the presence of these impairments. The NMSE expression is verified through numerical simulations.     

Fluorescence Techniques for Determination of the Membrane Potentials in High Throughput Screening

The characterization of small molecules requires identification and evaluation of several predictive parameters, when selecting compounds for pharmacological applications and/or determining their toxicity. A number of them are correlated with the compound interaction with biological membranes and/or capacity to cross them. The knowledge of the extent of adsorption, partition coefficient and permeability along with the compound ability to alter membrane properties are critical for such studies. Lipid bilayers are frequently used as the adequate experimental models of a biological membrane despite their simple structure and a limited number of components. A significant number of the biologically relevant lipid bilayer properties are related to its electrostatics. Three electrostatic potentials were defined for the lipid bilayer; the intrinsic or induced surface electrostatic potential, the dipole potential and the membrane potential. Each of them was measured with dedicated methodologies. The complex measurement protocols and technically demanding instrumentation made the development of efficient HTS approaches for complete characterization of membrane electrostatics practically impossible. However, the rapid development of fluorescence techniques accompanied by rapid growth in diversity and number of dedicated fluorescent probes enabled characterization of lipid bilayer electrostatics in a moderately simple manner. Technically advanced, compact and automated workstations, capable of measuring practically all fluorescence parameters, are now available. Therefore, the proper selection of fluorescent probes with measuring procedures can be designed to evaluate drug candidates in context of their ability to alter membrane electrostatics. In the paper we present a critical review of available fluorescence methods, useful for the membrane electrostatics evaluation and discuss the feasibility of their adaptation to HTS procedures. The significance of the presented methodology is even greater considering the rapid growth of advanced drug formulations, where electrostatics is an important parameter for production processes and pharmacokinetics of the product. Finally, the potential of the membrane electrostatics to emerge as a viable pharmacological target is indicated and fluorescence techniques capable to evaluate this potential are presented.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

Inelastic neutron scattering and lattice dynamics of minerals

We review current research on minerals using inelastic neutron scattering and lattice dynamics calculations. Inelastic neutron scattering studies in combination with first principles and atomistic calculations provide a detailed understanding of the phonon dispersion relations, density of states and their manifestations in various thermodynamic properties. The role of theoretical lattice dynamics calculations in the planning, interpretation and analysis of neutron experiments are discussed. These studies provide important insights in understanding various anomalous behaviour including pressure-induced amorphization, phonon and elastic instabilities, prediction of novel high pressure phase transitions, high pressure-temperature melting, etc.      

Phase Separation of Penetrable Core Mixtures

A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the random phase approximation (RPA) and the hypernetted chain (HNC) integral equation. The analytical RPA predictions are in semi-quantitative agreement with the numerical solutions of the HNC approximation, which itself is very accurate for gaussian core systems. A fluid-fluid phase separation is predicted to occur for a broad range of potential parameters. The pair structure exhibits a nontrivial clustering behaviour of the minority component. Similiar conclusions hold for the related model of parabolic core mixtures, which is frequently used in dissipative particle dynamics (DPD) simulations.     

Dissipative particle dynamics simulation on the rheological properties of heavy crude oil

The rheological properties of heavy crude oil have a significant impact on the production, refining and transportation. In this paper, dissipative particle dynamics (DPD) simulations were performed to study the effects of the addition of light crude oil and emulsification on the rheological properties of heavy crude oil. The simulation results reflected that the addition of light crude oil reduced the viscosity effectively. The shear thinning behaviour of crude oil mixtures were becoming less distinct as the increase of the mass fraction of light crude oil. According to the statistics, the shear had an influence on the aggregation and spatial orientation of asphaltene molecules. In addition, the relationship between the viscosity and the oil mass fraction was investigated in the simulations of emulsion systems. The viscosity increased with the oil mass fraction slowly in oil-in-water emulsions. When the oil mass fraction was higher than 50%, the increase became much faster since systems had been converted into water-in-oil emulsions. The equilibrated morphologies of emulsion systems were shown to illustrate the phase inversion. The surfactant-like feature of asphaltenes was also studied in the simulations.     

The synchronization method for fractional-order hyperchaotic systems

In this paper, a function cascade synchronization method for fractional-order hyperchaotic systems is introduced to achieve the synchronization of two identical fractional-order hyperchaotic systems. It is shown that the method is not only theoretically rigorous, practically feasible, but also a more general one, which contains the complete synchronization, modified projective synchronization and anti-phase synchronization. In order to valid the effectiveness of the proposed method, we give two illustrative examples. Suitable controllers are designed and the function cascade synchronization for fractional-order hyperchaotic systems is achieved. Numerical simulations are performed and shown to fit with our analysis results.     

On extending and optimising the direct product decomposition

Abstract

The concept of the direct product decomposition (DPD) is extended to arbitrary tensors while maintaining the same theoretical reduction in storage and computation. Additionally, the structure of the DPD as introduced by Gauss and Stanton is shown to be but one of a family of direct product decompositions which may be visualised using graphs. One particular member of this family is also shown to be critically important in relating the DPD and symmetry blocking approaches. Lastly, an implementation of tensor contraction using this extended DPD based on recent work in dense tensor contraction is presented, showing how the particular DPD used to represent the tensors in memory or on disk may be divorced from the optimal DPD used for a particular tensor contraction. The performance of the new algorithm is benchmarked by interfacing with the CFOUR programme suite, where significant speedups for CCSD calculations are observed.     

Extended theoretical analysis of crystallisation kinetics being studied by in situ XRD

ABSTRACT

Theoretical simulations were used to study the consequences of simplifying the replacement of the step-wise in situ X-ray diffraction (XRD) temperature programme by simple linear heating (at corresponding effective heating rate) during the kinetic calculations based on the multivariate kinetic analysis. The simulations were performed for a large variety of step-wise non-isothermal in situ XRD temperature programmes, covering most practically used combinations of the temperature step magnitude ΔT, rate of heating, and duration of the isothermal hold Δt. To achieve the universal interpretation of the obtained results, the behaviour of the majority of crystallisation processes with commonly encountered kinetic profiles was explored: simulations were performed for single-process transformations with highly negative, symmetric and highly positive asymmetries; complex multi-process reactions with different degrees of sub-process overlaps and variable activation energy were analysed. It was found that the asymmetry and shape of the crystallisation peaks do not significantly influence the level of distortion of kinetic parameters. The main factors that increase the errors of in situ XRD kinetic evaluations are high Δt, high ΔT and high activation energy (with the latter two being most important). Findings were discussed for the accuracy of the corresponding kinetic predictions. Generalisation of the present conclusions towards their universal utilisation for optimisation of in situ XRD experiments was suggested.     

Missing 2k(F) response for composite fermions in phonon drag

The conventional approach to treat charged defects in extended systems in first principles calculations is via the supercell approximation using a neutralizing jellium charge. I explicitly show that errors in the resulting electrostatic potential surface are comparable to a band gap energy in semiconductors, for cell sizes typically used in simulations. I present a method for eliminating divergence of the Coulomb potential in charged supercell calculations that correctly treats the electrostatic potential in the local vicinity of a charged defect, via a mixed boundary condition approach.     

First-principles thermodynamics of coherent interfaces in samarium-doped ceria nanoscale superlattices

Nanoscale superlattices of samarium-doped ceria layers with varying doping levels have been recently proposed as a novel fuel cell electrolyte. We calculate the equilibrium composition profile across the coherent {100} interfaces present in this system using lattice-gas Monte Carlo simulations with long-range interactions determined from electrostatics and short-range interactions obtained from ab initio calculations. These simulations reveal the formation of a diffuse, nonmonotonic, and surprisingly wide (11 nm at 400 K) interface composition profile, despite the absence of space charge regions.     

Self-Assembly Behavior of Amphiphilic Copolymer Characterized by Dissipative Particle Dynamics Simulation

Amphiphilic polyacrylamide copolymer aqueous solutions have a special behavior of self-assembly, which is attributed to their composition and molecular structure. In this work, methoxy polyethylene glycol acrylate (PEGA) and/or dodecafluoroheptyl methacrylate (DF) were introduced into the partially hydrolyzed polyacrylamide (HDPAM) molecular chains to enhance their hydrophilicity and hydrophobicity, respectively. The self-assembly behaviors of these copolymers in water solution and salt solution were studied by dissipative particle dynamics (DPD). Results showed that the amphiphilic copolymer (HDPAM-PEGA-DF) had a stronger self-assembly behavior than the hydrophobic modified polyacrylamide copolymer (HDPAM-DF).     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.