Rigorous Monte Carlo Simulations Research Articles

Microcanonical Monte Carlo of Lennard-Jones microclusters.

A novel statistical mechanical methodology is applied to clusters of N ≤ 7 atoms. Exact statistical analogs for any energy derivative of entropy ∂mS/∂Em are used in rigorous microcanonical Monte Carlo simulations to vastly enlarge the pool of measurable thermodynamic properties relative to previous work. All analogs are given for two alternative partition functions of the microcanonical ensemble. Coarse grained energy distributions are used to establish the existence of melting transitions. LJ7, LJ5, and LJ4 are found to exhibit trimodal distributions, a feature not being reported before. Varieties of combinations of entropy derivatives are tested for a direct detection of the melting region. It is shown that for such a purpose, derivatives of at least fourth order are necessary.

Effectiveness of Guard Zone in Mitigating Interference in D2D Underlaid Cellular Networks

Device-to-device (D2D) communications, a promising technology, let cellular devices that are close to each other connect with one another directly, by passing the network infrastructure. As such, the technology provides the cellular network with many benefits, such as higher sum data rates, lower latency, extended coverage, higher energy efficiency, added security, higher spectral efficiency, and more useful services like inexpensive file caching. However, it comes with a cost—the interference underlaid D2D users inflict on cellular users at the base station when both use the same uplink frequency, which is the prefered reuse mode. This cost can, however, be reduced using a guard zone—a disk around the base station (BS) where D2D communications are not allowed. This simple and easy to implement approach, which has unfortunately not received enough research attention, is demonstrated in the present article to be highly effective in reducing the interference to cellular users. We leverage for this demonstration the mathematical tool of stochastic geometry. With the assumption that the BSs are distributed as a Poisson point process (PPP), we construct an analytical model to characterize the coverage probability of the cellular user in the presence of D2D nodes. The numerical results obtained, which are validated by rigorous Monte Carlo simulations, confirm that the guard zone approach is highly effective in protecting the cellular user from potential D2D interference.

Sensing Mechanisms of Rough Plasmonic Surfaces for Protein Binding of Surface Plasmon Resonance Detection.

Surface plasmon resonance (SPR) has been utilized in various optical applications, including biosensors. The SPR-based sensor is a gold standard for protein kinetic measurement due to its ultrasensitivity on the plasmonic metal surface. However, a slight change in the surface morphology, such as roughness or pattern, can significantly impact its performance. This study proposes a theoretical framework to explain sensing mechanisms and quantify sensing performance parameters of angular surface plasmon resonance detection for binding kinetic sensing at different levels of surface roughness. The theoretical investigation utilized two models, a protein layer coating on a rough plasmonic surface with and without sidewall coatings. The two models enable us to separate and quantify the enhancement factors due to the localized surface plasmon polaritons at sharp edges of the rough surfaces and the increased surface area for protein binding due to roughness. The Gaussian random surface technique was employed to create rough metal surfaces. Reflectance spectra and quantitative performance parameters were simulated and quantified using rigorous coupled-wave analysis and Monte Carlo simulation. These parameters include sensitivity, plasmonic dip position, intensity contrast, full width at half maximum, plasmonic angle, and figure of merit. Roughness can significantly impact the intensity measurement of binding kinetics, positively or negatively, depending on the roughness levels. Due to the increased scattering loss, a tradeoff between sensitivity and increased roughness leads to a widened plasmonic reflectance dip. Some roughness profiles can give a negative and enhanced sensitivity without broadening the SPR spectra. We also discuss how the improved sensitivity of rough surfaces is predominantly due to the localized surface wave, not the increased density of the binding domain.

Acceptance sampling plans for the three-parameter inverted Topp-Leone model.

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp-Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp-Leone (TPITL) distribution. The power inverted Topp-Leone and the inverted Topp-Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp-Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences

The purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy-tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. The current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy-tailed data. The proposed family of distributions is known as the Arctan-X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan-Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan-Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. The Arctan-Weibull model is demonstrated using a real-world insurance data set. The Arctan-Weibull is compared to well-known two-, three-, and four-parameter competitors. Among the competing distributions are Weibull, Kappa, Burr-XII, and beta-Weibull. For model comparison, we used the most precise tests used to know whether the Arctan-Weibull distribution is more useful than competing models.

VFD-NOMA Under Imperfect SIC and Residual Inter-Relay Interference Over Generalized Nakagami-m Fading Channels

Full-duplex (FD) non-orthogonal multiple access (NOMA) communications is a promising technology to enhance spectral efficiency in future wireless access network. However, self-interference cancellation in FD is still a major challenge and thus concept of virtual full-duplex (VFD) relaying has evolved recently. In this letter, we investigate the impact of imperfect successive interference cancellation and residual inter-relay interference on a decode-and-forward relaying based VFD-NOMA. Framework for outage probability (OP), asymptotic OP, and ergodic rate expressions is developed for the considered system model over generalized Nakagami-m fading channels. Accuracy of the derived closed-form expressions is verified through rigorous Monte-Carlo simulations.

MIMO Radar Array Configuration with Enhanced Degrees of Freedom and Increased Array Aperture

This paper presents a new antenna array design approach for multiple-input multiple-output (MIMO) radar. The geometry exhibits increased degrees of freedom (DOFs) with precise antenna locations for direction-of-arrival (DOA) estimation of sources. The enhancement is realized by using the method of sum coarray of the difference coarray (SCDC). By effectively increasing the inter-element spacing of the transmitting array, a larger hole-free SCDC uniform linear array (ULA) is obtained. This increment provides more DOFs and extended virtual array aperture (VAA) for intended geometry. The transmitting and receiving sensor positions are based on the maximum inter-element spacing constraint (MISC) principle. The MISC composition involves three sparse ULAs with two separate antennas placed appropriately. The mathematical expressions are presented to validate the designed model. Moreover, arbitrary and optimized antenna scenarios for the transmitter and receiver are investigated in terms of DOFs and VAA. The advantages of the proposed configuration are demonstrated by conducting rigorous Monte Carlo simulations. The experimental results of DOFs, VAA, number of resolvable sources, Cram $$\acute{\hbox {e}}$$ r–Rao bound performance, detection, and resolution ability reveal that the proposed sensor array design approach is suitable for MIMO radar which is also capable of estimating the DOAs of multiple sources efficiently in underdetermined scenarios.

Inductor-less PVT robust gain switching balun LNA for multistandard applications

ABSTRACTAn inductor-less single to differential low-noise amplifier (LNA) is proposed for multistandard applications in the frequency band of 0.2–2 GHz. The proposed LNA incorporates noise cancellation and voltage shunt feedback configuration to achieve minimum noise characteristics and low power consumption. In addition to noise cancellation, trans-conductance of common-source stage is scaled to improve the noise performance. In this way, noise figure (NF) of LNA below 3 dB is achieved. An additional capacitor Cc is used to correct the gain and phase imbalance at the output. The gain switching has been enabled with a step size of 4 dB for high linearity and power efficiency. The bias point of all transistors is chosen such that the variation in gm is not more than 10%. The proposed LNA is implemented in UMC 0.18-μm RF CMOS technology. The core area is 182 μm × 181 μm. Moreover, the LNA has better ratio of relevant performance to area. The proposed balun LNA is validated by rigorous Monte Carlo simulation. The 3σ deviation of gain and NF is less than 5%. Finally, the proposed LNA is robust to unavoidable PVT variations.

Microcanonical thermodynamics of three and four atoms.

Clusters are treated in the microcanonical ensemble. Two classical choices for the partition function are used in Boltzmann's assumption for entropy: Phase space volume and phase space density. For both definitions, exact statistical analogs are derived for energy derivatives of entropy to arbitrary order. The analogs are used in rigorous microcanonical Monte Carlo simulation to measure entropy derivatives up to order three for systems of three and four atoms. All simulation results are confirmed by direct numerical integration of the statistical analogs.

Quantifying uncertainties in signal position in non-resolved object images: Application to space object observation

Charged Coupled Devices (CCDs) and subsequently Complementary metal-oxide-semiconductor (CMOS) detectors revolutionized scientific imaging. On both the CCD and CMOS detector, the generated images are degraded by inevitable noise. In many applications, such as in astronomy or for satellite tracking, only unresolved object images are available. Strategies to estimate the center of the non-resolved image their results are affected by the detector noise. The uncertainty in the center is classically estimated by running prohibitively costly Monte Carlo simulations, but in this paper, we propose analytic uncertainty estimates of the center position. The expressions that depend on the pixel size, the signal to noise ratio and the extension of the object signal relative to the pixel size are validated against rigorous Monte Carlo simulations with very satisfying results. Numerical tests show that our analytic expression is an efficient substitute to the Monte Carlo simulation thereby reducing computational cost.

Structure Sensitivity of Electrochemical Reactions from First Principles: Applications to Nitrogen and Water Cycles

Nitrogen cycle electrochemistry is an emerging area of interest in the electrocatalysis community, with applications ranging from removal of nitrates from wastewater streams to the development of fundamental understanding of NO electrochemistry. In spite of a significant amount of fundamental research for this chemistry on single crystal surfaces, however, the mechanistic details of the reactions are not fully known, and even such basic information as the nature of the rate-limiting step is not understood. In this work, we apply some of the innovations in theoretical electrochemistry that have emerged over the past 5-10 years to the study of NO and nitrate reduction on transition metal surfaces. We begin with a simple Density Functional Theory analysis of direct NO reduction in acid on Pt(111), Pt(100), and Pt(211) surfaces, and we identify potential- and rate-determining steps on each surface, using extensive ab-initio molecular dynamics simulations to estimate the impact of the aqueous environment on surface thermodynamics and kinetics (Ang. Chem. Int. Ed. 2015). We next introduce a novel approach that couples DFT calculations with rigorous kinetic Monte Carlo (kMC) simulations to understand, in unprecedented detail, the effect of higher adsorbed NO coverages on these chemistries, and we demonstrate that these coverage-dependent effects are essential for describing experimentally measured polarization curves (ACS Catalysis 2017). We subsequently generalize our analysis by developing universal Brønsted-Evans-Polanyi relationships that rigorously relate barriers for proton-coupled electron transfer to surface species to the corresponding thermodynamics across a large space of different transition metals and potentials. These relationships, combined with the potential- and coverage-dependent energetics determined on platinum, provide a basis to extrapolate our mechanistic analyses to other transition metals, including PtSn and related alloys. We employ these techniques to propose design strategies to tune selectivity of NO electroreduction to desired products, including N2 and hydroxylamine, on these different transition metals and alloys. If time permits, we will briefly describe some additional work on the development of structural and catalytic reactivity models at the interface between thin hydroxyoxide films and precious metal platinum substrates. We will examine the kinetics of the hydrogen evolution reaction as a function of the structure and oxidation state of these interfaces and will demonstrate that the bifunctional nature of the interfaces plays a key role in their electrocatalytic properties.

Is the error on first-principles volume predictions absolute or relative?

Many benchmarks of density-functional theory with respect to experiment suggest the error on predicted equilibrium volumes to scale with the volume. Relative volume errors are therefore often used as a decisive argument to select one exchange–correlation functional over another. We show that the error on the volume (after correcting for systematic deviations) is only approximately relative. A simple analytic model, validated by rigorous Monte Carlo simulations, reveals that a more accurate error estimate can be derived from the inverse of the bulk modulus. This insight is not only instrumental for the selection or design of suitable functionals. It also calls for a new attitude towards computational errors: to report computational errors on electronic-structure calculations, identify systematic deviations and distinguish between relative and absolute effects.

Statistical Modeling and Performance Characterization of Ultrashort Light Pulse Communication System Using Power-Cubic Optical Nonlinear Preprocessor

In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y, which is formed at the output of the power-cubic all-optical nonlinear preprocessor followed by the photodetector, with applications in ultrafast optical time-division multiplexing and optical code-division multiple-access systems. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte Carlo simulation, the accuracy of the widely used Gaussian approximation of decision variable Y is refuted. However, in this paper, we show that the so-called log-Pearson type-3 (LP3) pdf is an excellent representation for the decision variable Y. Three distinguishable parameters of the LP3 pdf are obtained through an analytical derivation of three moments of the decision variable Y. Furthermore, toward a more realistic model, in addition to amplified spontaneous emission Gaussian noise, the effects of shot and thermal noises are also included. Finally, using the presented analytical approach, it is shown that the power-cubic preprocessor outperforms its quadratic counterparts, i.e., second-harmonic-generation and two-photon-absorption devices, in the high-power regime where shot and thermal noises can be neglected.

Robust Pilot Detection Techniques for Channel Estimation and Symbol Detection in OFDM Systems

In this letter, we propose new frequency-domain pilot-multiplexing techniques (FDPMTs) for the channel estimation and equalization in orthogonal frequency-division multiplexing (OFDM) systems. A robust and effective pilot insertion and detection scheme is devised thereby. These pilot positions are optimally selected to minimize the distortion of the transmitted time-domain signal caused by the subcarrier-removal at the corresponding pilot positions. Besides, three different blind pilot-detection techniques are designed at the receiver without any a priori knowledge of the pilot positions, and the distorted data symbols can thus be iteratively reconstructed. Rigorous theoretical analysis and Monte Carlo simulation results both demonstrate that our proposed new OFDM system using dynamical pilot positions is more robust than the conventional OFDM system using the fixed pilot positions over multipath fading channels.

Understanding the relationship between true and measured resist feature critical dimension and line edge roughness using a detailed scanning electron microscopy simulator

Top-down critical dimension scanning electron microscopy (SEM) is still the workhorse metrology tool used for nanoscale structure analysis, such as measurement of photoresist features, during integrated circuit manufacturing. However, the degree to which top-down SEM imaging can accurately be used to quantitatively determine the size, shape, and roughness characteristics of three-dimensional structures such as photoresist features has not been carefully characterized. A rigorous Monte Carlo simulation of scanning electron microscopy has been developed to probe the relationship between the roughness of a three-dimensional feature and the line edge roughness (LER) as measured by SEM. The model uses the differential Mott cross section to compute elastic scattering, while inelastic scattering and secondary electron generation are handled using dielectric function theory. The model can calculate the electron scattering for any arbitrary three-dimensional geometry. Experimental SEM measurements of photoresist nanostructures show good agreement with the simulation output. The critical dimension of the resist determined from SEM best matches the true resist feature width when the line edge is defined using a high image threshold because the roughness on the outer edge of the resist tends to cause an increase in SEM signal that is nonproportional to the amount of material on the outer edge of the feature. LER determined from SEM was found to be significantly smaller than the true resist feature sidewall roughness. The measured LER is typically greater than 50% smaller than the actual sidewall roughness.

Terahertz emission from InAs induced by photo-Dember effect: Hydrodynamic analysis and Monte Carlo simulations

Terahertz emission from InAs excited by the femtosecond optical pulse is investigated. The hydrodynamic model is developed for the simplified analysis of the terahertz emission induced by the photo-Dember effect. The hydrodynamic model predicts that the amplitude of the transient photocurrent is proportional to the difference between the squared velocities of photoexcited electrons and holes. The predictions of the hydrodynamic model are compared to the results of the rigorous ensemble Monte Carlo simulations. The dependences of the intensity of terahertz emission on the optical fluence, on the photon energy, and on the optical pulse duration are studied. At low intensities of the optical pulse, the emitted terahertz energy is proportional to the power ranging between 3/2 and 2 of the optical pulse intensity. The emitted terahertz energy saturates at high intensities of the optical pulse. The spectral dependence of the terahertz emission from InAs is investigated. It is found that the intensity of terahertz emission profoundly depends on the optical pulse duration.

Modeling of Alpha-Induced Single Event Upsets for 45 nm Node SOI Devices Using Realistic C4 and 3D Circuit Geometries

Novel techniques have been applied to model realistic alpha particle source distributions in complex back-end-of-the-line geometries. Rigorous Monte Carlo simulations with high resolution have been performed to analyze the charge collection in 45 nm SOI test devices. These studies reveal soft fail sensitivity to the topologies of the alpha particle source and the BEOL structure.

Thermodynamics and entanglements of walks under stress

We use rigorous arguments and Monte Carlo simulations to study the thermodynamics and thetopological properties of self-avoiding walks on the cubic lattice subjected to an external forcef. The walks are anchored at one or both endpoints to an impenetrable plane atZ = 0 and the force isapplied in the Z-direction. If a force is applied to the free endpoint of an anchored walk, then a model ofpulled walks is obtained. If the walk is confined to a slab and a force is applied to the topbounding plane, then a model of stretched walks is obtained. For both models we provethe existence of the limiting free energy for any value of the force and we showthat, for compressive forces, the thermodynamic properties of the two modelsdiffer substantially. For pulled walks we prove the existence of a phase transitionthat, by numerical simulation, we estimate to be second order and located atf = 0. By using a pattern theorem for large positive forces we show that almost all sufficientlylong stretched walks are knotted. We examine the entanglement complexity of stretchedand pulled walks; our numerical results show a sharp reduction with increasing pulling andstretching forces. Finally, we also examine models of pulled and stretched loops. Weprove the existence of limiting free energies in these models and consider the knotprobability numerically as a function of the applied pulling or stretching force.

Haze of surface random systems: An approximate analytic approach

Approximate analytic expressions for haze (and gloss) of Gaussian randomly rough surfaces for various types of correlation functions are derived within phase-perturbation theory. The approximations depend on the angle of incidence, polarization of the incident light, the surface roughness, $\ensuremath{\sigma}$, and the average of the power spectrum taken over a small angular interval about the specular direction. In particular it is demonstrated that haze (gloss) increase (decrease) with $\ensuremath{\sigma}/\ensuremath{\lambda}$ as $\text{exp}[\ensuremath{-}A{(\ensuremath{\sigma}/\ensuremath{\lambda})}^{2}]$ and decreases (increase) with $a/\ensuremath{\lambda}$, where $a$ is the correlation length of the surface roughness, in a way that depends on the specific form of the correlation function being considered. These approximations are compared to what can be obtained from a rigorous Monte Carlo simulation approach, and a good agreement is found over large regions of parameter space. Some experimental results for the angular distribution of the transmitted light through polymer films and their haze are presented and compared to the analytic approximations derived in this paper. A satisfactory agreement is found. In the literature haze of blown polyethylene films has been related to surface roughness. Few authors have quantified the roughness and others have pointed to the difficulty in finding the correct roughness measure.

Characterization of thin-foil ultracold neutron detectors

We have fabricated ultracold neutron detectors that consist of silicon charged particle detectors coupled with thin nickel foils coated with either natural LiF or 10B implanted into vanadium. The foils convert neutrons into energetic, readily detectable, charged particles which are in turn detected by silicon detectors. The detectors were tested at the Institut Laue-Langevin with a gravitational spectrometer. From a rigorous Monte Carlo simulation of the experiment, the minimum detection cutoff velocities (effective potentials) were determined to be 309 ± 17 cm / s ( 49.8 ± 2.7 neV ) for LiF and 367 ± 39 cm / s ( 70.3 ± 7.5 neV ) for 10B/V. Although the result for LiF is consistent with expectations, the result for 10B/V is significantly higher. We interpret this discrepancy as due to contamination. We also show that while a thicker foil is more efficient for ultracold neutron detection, a thinner foil is more ideal for determining the cutoff velocity.