Frontiers in Physics | Computational Physics section | New and Recent Articles
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RSS Feed for Computational Physics section in the Frontiers in Physics journal | New and Recent Articlesen-usFrontiers Feed Generator,version:12020-03-31T03:09:44.7400312+00:0060https://www.frontiersin.org/articles/10.3389/fphy.2020.00042
https://www.frontiersin.org/articles/10.3389/fphy.2020.00042
Physics-Informed Neural Networks for Cardiac Activation Mapping2020-02-28T00:00:00ZFrancisco Sahli CostabalYibo YangParis PerdikarisDaniel E. HurtadoEllen KuhlA critical procedure in diagnosing atrial fibrillation is the creation of electro-anatomic activation maps. Current methods generate these mappings from interpolation using a few sparse data points recorded inside the atria; they neither include prior knowledge of the underlying physics nor uncertainty of these recordings. Here we propose a physics-informed neural network for cardiac activation mapping that accounts for the underlying wave propagation dynamics and we quantify the epistemic uncertainty associated with these predictions. These uncertainty estimates not only allow us to quantify the predictive error of the neural network, but also help to reduce it by judiciously selecting new informative measurement locations via active learning. We illustrate the potential of our approach using a synthetic benchmark problem and a personalized electrophysiology model of the left atrium. We show that our new method outperforms linear interpolation and Gaussian process regression for the benchmark problem and linear interpolation at clinical densities for the left atrium. In both cases, the active learning algorithm achieves lower error levels than random allocation. Our findings open the door toward physics-based electro-anatomic mapping with the ultimate goals to reduce procedural time and improve diagnostic predictability for patients affected by atrial fibrillation. Open source code is available at https://github.com/fsahli/EikonalNet.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00030
https://www.frontiersin.org/articles/10.3389/fphy.2020.00030
Deep Learning Over Reduced Intrinsic Domains for Efficient Mechanics of the Left Ventricle2020-02-26T00:00:00ZGonzalo D. Maso TalouThiranja P. Babarenda GamageMark SagarMartyn P. NashCardiac mechanics tools can be used to enhance medical diagnosis and treatment, and assessment of risk of cardiovascular diseases. Still, the computational cost to solve cardiac models restricts their use for online applications and routine clinical practice. This work presents a surrogate model obtained by training a set of Siamese networks over a physiological representation of the left ventricle. Our model allows us to modify the geometry, loading conditions, and material properties without needing of retraining. Additionally, we propose the novel concept of intrinsic domain that improves the accuracy of the network predictions by one order of magnitude. The neural networks were trained and tested with numerical predictions from a previously published finite element model of the left ventricle. Different loading conditions, material properties and geometrical definitions of the domain were simulated by the model leading to a dataset of 5, 670 cases. In terms of accuracy and performance, the surrogate model approximates the displacement field of the finite element model with an error of 4.4 ± 2.9% (with respect to the L_{2}-norm of the true displacement field) across all cases while performing computations 62 times faster. Hence, the trained model is capable of computing a passive cardiac filling of the chamber at 10 different time points in just ~0.7 s. These outcomes prove usability of training surrogate models for efficient simulations to facilitate the use of complex mechanical models in clinical practice for therapeutic planning and online diagnosis.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00247
https://www.frontiersin.org/articles/10.3389/fphy.2019.00247
Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations2020-01-21T00:00:00ZRitvik VasanMeagan P. RowanChristopher T. LeeGregory R. JohnsonPadmini RangamaniMichael HolstIn this perspective, we examine three key aspects of an end-to-end pipeline for realistic cellular simulations: reconstruction and segmentation of cellular structures; generation of cellular structures; and mesh generation, simulation, and data analysis. We highlight some of the relevant prior work in these distinct but overlapping areas, with a particular emphasis on current use of machine learning technologies, as well as on future opportunities.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00235
https://www.frontiersin.org/articles/10.3389/fphy.2019.00235
A Deep Learning Approach to Predict Abdominal Aortic Aneurysm Expansion Using Longitudinal Data2020-01-15T00:00:00ZZhenxiang JiangHuan N. DoJongeun ChoiWhal LeeSeungik BaekAn abdominal aortic aneurysm (AAA) is a gradual enlargement of the aorta that can cause a life-threatening event when a rupture occurs. Aneurysmal geometry has been proved to be a critical factor in determining when to surgically treat AAAs, but, it is challenging to predict the patient-specific evolution of an AAA with biomechanical or statistical models. The recent success of deep learning in biomedical engineering shows promise for predictive medicine. However, a deep learning model requires a large dataset, which limits its application to the prediction of the patient-specific AAA expansion. In order to cope with the limited medical follow-up dataset of AAAs, a novel technique combining a physical computational model with a deep learning model is introduced to predict the evolution of AAAs. First, a vascular Growth and Remodeling (G&R) computational model, which is able to capture the variations of actual patient AAA geometries, is employed to generate a limited in silico dataset. Second, the Probabilistic Collocation Method (PCM) is employed to reproduce a large in silico dataset by approximating the G&R simulation outputs. A Deep Belief Network (DBN) is then trained to provide fast predictions of patient-specific AAA expansion, using both in silico data and patients' follow-up data. Follow-up Computer Tomography (CT) scan images from 20 patients are employed to demonstrate the effectiveness and the feasibility of the proposed model. The test results show that the DBN is able to predict the enlargements of AAAs with an average relative error of 3.1%, which outperforms the classical mixed-effect model by 65%.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00203
https://www.frontiersin.org/articles/10.3389/fphy.2019.00203
First-Principles Calculation of Physical Tensors of α-Diisopropylammonium Bromide (α-DIPAB) Molecular Ferroelectric Crystal2019-11-29T00:00:00ZAhmad AlsaadNabil Al-AqtashRenat F. SabirianovAhmad AhmadQais M. Al-BatainehIssam QattanZaid AlbatainehWe report accurate calculations of tonsorial elements of α-Diisopropylammonium bromide (α-DIPAB) molecular ferroelectric crystal. In particular, elastic, piezoelectric and dielectric tensors were computed using density functional theory (DFT)-based Vienna ab initio simulation package (VASP). The determination of above parameters allows an accurate description of the energy landscape for modeling of realistic devices at finite temperatures. We determine the major physical tensors in energy expansion of total energy per volume of un-deformed crystal to provide experimentalists with valuable information for designing and fabrication of pyroelectric detectors, capacitors, piezoelectric devices based on α-DIPAB. The spontaneous polarization P_{s} was calculated using Berry phase approach and found to be 22.64 μC/cm^{2} in agreement with reported theoretical value. Furthermore, we calculate dynamical Born effective charge tensor to get a deeper insight into the bonding network and lattice dynamic of α-DIPAB crystal. The neighboring layers of DIPA molecules were found to be strongly crenelated due to the strong short-ranged electrostatic repulsion between Br sites in the DIPAB crystal structure. The organization of species in DIPA molecular layer as well as in the bromine “stitching” layer is essential for accurate calculation of DIPAB elastic properties. Having understood the actual network bonding in α-DIPAB, we calculated the components of the elastic moduli tensor. Our results indicate that a Young's modulus of 50–150 GPa and a shear modulus of 4–26 GPa were found. Thus, α-DIPAB phase has a great potential to be a terrific candidate for flexible electronic device applications. The value of the principle component of electronic contribution to the static dielectric tensor of α-DIPAB is found to be ≈2.5, i.e., 50% smaller than that in typical perovskite-based ferroelectrics. Therefore, α-DIPAB is anticipated to exhibit creative materials' innovations. It could be potential candidate as insulating layer of polymer thick films. Its mechanical, insulating and elastic properties make it eligible for switch keys and flex-circuit applications. Furthermore, clamped-ion piezoelectric tensor is calculated. Our results indicate a reasonable piezoelectric response of this polar crystal making it a low cost attractive candidate for piezoelectric applications.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00187
https://www.frontiersin.org/articles/10.3389/fphy.2019.00187
Dynamics of the Fluctuating Flying Chain2019-11-19T00:00:00ZEirik G. FlekkøyMarcel MouraKnut Jørgen MåløyA chain which is made to flow from a container, forms a striking arch that rises well above the container top. This phenomenon is caused by the well known Mould effect and is explained by a supply of momentum from the container, causing an upwards kick. Here we introduce a theory that allows for dynamic fluctuations of the chain and compare with corresponding simulations and experiments. The predictions for the chain velocity and fountain height agree well with experiments. We also explore the underlying mechanism for this momentum transfer for different chain models and find that it depends subtly on the nature of the chain as well as on the container.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00154
https://www.frontiersin.org/articles/10.3389/fphy.2019.00154
Fluocell for Ratiometric and High-Throughput Live-Cell Image Visualization and Quantitation2019-10-23T00:00:00ZQin QinShannon LaubYiwen ShiMingxing OuyangQin PengJin ZhangYingxiao WangShaoying LuSpatiotemporal regulation of molecular activities dictates cellular function and fate. Investigation of dynamic molecular activities in live cells often requires the visualization and quantitation of fluorescent ratio image sequences with subcellular resolution and in high throughput. Hence, there is a great need for convenient software tools specifically designed with these capabilities. Here we describe a well-characterized open-source software package, Fluocell, customized to visualize pixelwise ratiometric images and calculate ratio time courses with subcellular resolution and in high throughput. Fluocell also provides group statistics and kinetic analysis functions for the quantified time courses, as well as 3D structure and function visualization for ratio images. The application of Fluocell is demonstrated by the ratiometric analysis of intensity images for several single-chain Förster (or fluorescence) resonance energy transfer (FRET)-based biosensors, allowing efficient quantification of dynamic molecular activities in a heterogeneous population of single live cells. Our analysis revealed distinct activation kinetics of Fyn kinase in the cytosolic and membrane compartments, and visualized a 4D spatiotemporal distribution of epigenetic signals in mitotic cells. Therefore, Fluocell provides an integrated environment for ratiometric live-cell image visualization and analysis, which generates high-quality single-cell dynamic data and allows the quantitative machine-learning of biophysical and biochemical computational models for molecular regulations in cells and tissues.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00117
https://www.frontiersin.org/articles/10.3389/fphy.2019.00117
Prediction of Left Ventricular Mechanics Using Machine Learning2019-09-06T00:00:00ZYaghoub DabiriAlex Van der VeldenKevin L. SackJenny S. ChoyGhassan S. KassabJulius M. GuccioneThe goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00097
https://www.frontiersin.org/articles/10.3389/fphy.2019.00097
Effect of Grain Boundary on Diffusion of P in Alpha-Fe: A Molecular Dynamics Study2019-07-12T00:00:00ZM. Mustafa AzeemQingyu WangYue ZhangShengbo LiuMuhammad ZubairIn this study, we have investigated the effect of the grain boundary (GB) on the diffusion of a Phosphorus (P) atom in alpha-Fe using molecular dynamics simulations. A Fe-P mixed <110> dumbbell is created in the six symmetric tilt grain boundary (STGB) models. The dumbbells are allowed to migrate at different temperatures from 400 to 1,000 K, with starting positions between 5 to 10Å away from the GB core. The trajectories and mean square displacements (MSD) have been recorded to analyze the diffusion details. The Nudged Elastic Band (NEB) method has been used to study the energy barrier at different positions around the GBs. Our simulation results demonstrate that the GB structure affects the diffusion mechanisms of Fe-P dumbbell. The two low Σ favored GBs display significantly weak trapping effect, which is consistent with the formation energy distribution. The reduction in the migration barrier has been observed due to the decrease of distance from the GB center. Furthermore, the barriers of migration toward the GB are lower than the barriers of migration away from the GB. As evident by NEB calculation, absorption sink effect of GB has been observed. This effect saturates as the distance reaches 8Å or more. Our simulation results provide an insight into the GB trapping effect in alpha-Fe.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00048
https://www.frontiersin.org/articles/10.3389/fphy.2019.00048
Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer2019-04-05T00:00:00ZMaliheh AramonGili RosenbergElisabetta ValianteToshiyuki MiyazawaHirotaka TamuraHelmut G. KatzgraberThe Fujitsu Digital Annealer is designed to solve fully connected quadratic unconstrained binary optimization (QUBO) problems. It is implemented on application-specific CMOS hardware and currently solves problems of up to 1,024 variables. The Digital Annealer's algorithm is currently based on simulated annealing; however, it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism. In addition, the Digital Annealer exploits the massive parallelization that custom application-specific CMOS hardware allows. We compare the performance of the Digital Annealer to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully connected spin-glass problems with bimodal and Gaussian couplings. These represent the respective limits of sparse vs. dense problems, as well as high-degeneracy vs. low-degeneracy problems. Our results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study. The Digital Annealer does not appear to exhibit a speedup for sparse two-dimensional spin-glass problems, which we explain on theoretical grounds. We also benchmarked an early implementation of the Parallel Tempering Digital Annealer. Our results suggest an improved scaling over the other algorithms for fully connected problems of average difficulty with bimodal disorder. The next generation of the Digital Annealer is expected to be able to solve fully connected problems up to 8,192 variables in size. This would enable the study of fundamental physics problems and industrial applications that were previously inaccessible using standard computing hardware or special-purpose quantum annealing machines.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00003
https://www.frontiersin.org/articles/10.3389/fphy.2019.00003
Phonon Transmission Across Silicon Grain Boundaries by Atomistic Green's Function Method2019-01-29T00:00:00ZChen LiZhiting TianNanostructured materials are of great interest for many applications because of their special properties. Understanding the effect of grain boundaries on phonon transport in polycrystals is important for engineering nanomaterials with desired thermal transport properties. The phonon transport properties of Σ3 grain boundaries in silicon are investigated by employing atomistic Green's function method. Results show that similar to electron transport, the perfect grain boundary does not significantly reduce the thermal conductance, while defective grain boundaries can dramatically reduce the thermal conductance. This work may be helpful for the understanding of the underlying thermal transport mechanism across grain boundaries and the design of grain boundaries for energy applications.]]>https://www.frontiersin.org/articles/10.3389/fphy.2018.00123
https://www.frontiersin.org/articles/10.3389/fphy.2018.00123
On Transient Response of Piezoelectric Transducers2018-11-06T00:00:00ZLin FaJinpeng MouYuxiao FaXin ZhouYandong ZhangMeng LiangPengfei DingShaojie TangHong YangQi ZhangMaomao WangGuihui LiMeishan ZhaoIn this paper, we report a new model in analysis of spherical thin-shell piezoelectric transducers for transient response, based on Fourier transform and the principle of linear superposition. We show that a circuit-network, a combination of a series of parallel-connected equivalent-circuits, can be used in description of a spherical thin-shell piezoelectric transducer. When excited by a signal with multiple frequency components, each circuit would have a distinctive radiation resistance and a radiation mass, arising from an individual frequency component. Each frequency component would act independently on the electric/mechanic-terminals. A cumulative signal-output from the mechanic/electric-terminals is measured as the overall acoustic/electric output. As a prototype example in testing the new model, we have designed two spherical shin-shell transducers, applied a gated sine electric-signal as the initial excitation, and recorded the experimental information. The transient response and the output signals are calculated based on the new model. The results of calculation are in good agreement with that of experimental observation.]]>https://www.frontiersin.org/articles/10.3389/fphy.2018.00084
https://www.frontiersin.org/articles/10.3389/fphy.2018.00084
Mechanisms of the Flying Chain Fountain2018-08-14T00:00:00ZEirik G. FlekkøyMarcel MouraKnut J. MåløyWhen a chain is released by one end from a container, it forms a striking arch extending well above the container. This phenomenon is caused by the famous Mould effect and is explained by an anomalous supply of momentum from the container, causing an upwards kick. Using simulations, experiments as well as theoretical arguments we explore the underlying mechanism for this momentum transfer and find that it depends subtly on the nature of the chain as well as on the container. Generally, it does not suffice to assume a model of the chain as a sequence of rigid elements that, due to angular moment conservation, kicks off from the container. Rather the structure of the underlying system must be included, and we analyze how this structure along with the chain mechanics may cause the required upwards force.]]>https://www.frontiersin.org/articles/10.3389/fphy.2018.00086
https://www.frontiersin.org/articles/10.3389/fphy.2018.00086
GTPack: A Mathematica Group Theory Package for Application in Solid-State Physics and Photonics2018-08-14T00:00:00ZR. Matthias GeilhufeWolfram HergertWe present the Mathematica group theory package GTPack providing about 200 additional modules to the standard Mathematica language. The content ranges from basic group theory and representation theory to more applied methods like crystal field theory, tight-binding and plane-wave approaches capable for symmetry based studies in the fields of solid-state physics and photonics. GTPack is freely available via http://GTPack.org. The package is designed to be easily accessible by providing a complete Mathematica-style documentation, an optional input validation and an error strategy. We illustrate the basic framework of the package and show basic examples to present the functionality. Furthermore, we give a complete list of the implemented commands including references for algorithms within the Supplementary Material.]]>https://www.frontiersin.org/articles/10.3389/fphy.2018.00056
https://www.frontiersin.org/articles/10.3389/fphy.2018.00056
Stable and Efficient Time Integration of a Dynamic Pore Network Model for Two-Phase Flow in Porous Media2018-06-13T00:00:00ZMagnus Aa. GjennestadMorten VassvikSigne KjelstrupAlex HansenWe study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number Ca, and at Ca~ 10^{−8} the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method.]]>https://www.frontiersin.org/articles/10.3389/fphy.2018.00030
https://www.frontiersin.org/articles/10.3389/fphy.2018.00030
Causal Scale of Rotors in a Cardiac System2018-04-10T00:00:00ZHiroshi AshikagaFrancisco Prieto-CastrilloMari KawakatsuNima DehghaniRotors of spiral waves are thought to be one of the potential mechanisms that maintain atrial fibrillation (AF). However, disappointing clinical outcomes of rotor mapping and ablation to eliminate AF raise a serious doubt on rotors as a macro-scale mechanism that causes the micro-scale behavior of individual cardiomyocytes to maintain spiral waves. In this study, we aimed to elucidate the causal relationship between rotors and spiral waves in a numerical model of cardiac excitation. To accomplish the aim, we described the system in a series of spatiotemporal scales by generating a renormalization group, and evaluated the causal architecture of the system by quantifying causal emergence. Causal emergence is an information-theoretic metric that quantifies emergence or reduction between micro- and macro-scale behaviors of a system by evaluating effective information at each scale. We found that the cardiac system with rotors has a spatiotemporal scale at which effective information peaks. A positive correlation between the number of rotors and causal emergence was observed only up to the scale of peak causation. We conclude that rotors are not the universal mechanism to maintain spiral waves at all spatiotemporal scales. This finding may account for the conflicting benefit of rotor ablation in clinical studies.]]>https://www.frontiersin.org/articles/10.3389/fphy.2017.00048
https://www.frontiersin.org/articles/10.3389/fphy.2017.00048
A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue2017-10-10T00:00:00ZAslak TveitoKaroline H. JægerMiroslav KuchtaKent-Andre MardalMarie E. RognesIn this paper, we study a mathematical model of cardiac tissue based on explicit representation of individual cells. In this EMI model, the extracellular (E) space, the cell membrane (M), and the intracellular (I) space are represented as separate geometrical domains. This representation introduces modeling flexibility needed for detailed representation of the properties of cardiac cells including their membrane. In particular, we will show that the model allows ion channels to be non-uniformly distributed along the membrane of the cell. Such features are difficult to include in classical homogenized models like the monodomain and bidomain models frequently used in computational analyses of cardiac electrophysiology. The EMI model is solved using a finite difference method (FDM) and two variants of the finite element method (FEM). We compare the three schemes numerically, reporting on CPU-efforts and convergence rates. Finally, we illustrate the distinctive capabilities of the EMI model compared to classical models by simulating monolayers of cardiac cells with heterogeneous distributions of ionic channels along the cell membrane. Because of the detailed representation of every cell, the computational problems that result from using the EMI model are much larger than for the classical homogenized models, and thus represent a computational challenge. However, our numerical simulations indicate that the FDM scheme is optimal in the sense that the computational complexity increases proportionally to the number of cardiac cells in the model. Moreover, we present simulations, based on systems of equations involving ~117 million unknowns, representing up to ~16,000 cells. We conclude that collections of cardiac cells can be simulated using the EMI model, and that the EMI model enable greater modeling flexibility than the classical monodomain and bidomain models.]]>https://www.frontiersin.org/articles/10.3389/fphy.2017.00034
https://www.frontiersin.org/articles/10.3389/fphy.2017.00034
Comparison of the Melting Temperatures of Classical and Quantum Water Potential Models2017-08-17T00:00:00ZSen DuSoohaeng YooJinjin LiAs theoretical approaches and technical methods improve over time, the field of computer simulations for water has greatly progressed. Water potential models become much more complex when additional interactions and advanced theories are considered. Macroscopic properties of water predicted by computer simulations using water potential models are expected to be consistent with experimental outcomes. As such, discrepancies between computer simulations and experiments could be a criterion to comment on the performances of various water potential models. Notably, water can occur not only as liquid phases but also as solid and vapor phases. Therefore, the melting temperature related to the solid and liquid phase equilibrium is an effective parameter to judge the performances of different water potential models. As a mini review, our purpose is to introduce some water models developed in recent years and the melting temperatures obtained through simulations with such models. Moreover, some explanations referred to in the literature are described for the additional evaluation of the water potential models.]]>https://www.frontiersin.org/articles/10.3389/fphy.2016.00028
https://www.frontiersin.org/articles/10.3389/fphy.2016.00028
Parameter Tuning for the NFFT Based Fast Ewald Summation2016-07-18T00:00:00ZFranziska NestlerThe computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P^{2}NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P^{3}M) algorithm. The publicly available P^{2}NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.]]>https://www.frontiersin.org/articles/10.3389/fphy.2015.00046
https://www.frontiersin.org/articles/10.3389/fphy.2015.00046
Minimalistic real-space renormalization of Ising and Potts Models in two dimensions2015-06-23T00:00:00ZGary WillisGunnar PruessnerJonathan KeelanWe introduce and discuss a real-space renormalization group (RSRG) procedure on very small lattices, which in principle does not require any of the usual approximations, e.g., a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4 × 4 to 2 × 2) and implemented for the Ising Model and the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3–7% of the exact values. The 4-state Potts Model generates a third magnetic exponent, which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q = 5 Potts Model.]]>