Statistical Physics Models Research Articles

Combined statistical physics models and DFT theory to study the adsorption process of paprika dye On TiO2 for dye sensitized solar cells

This study reported the combination of advanced statistical physics modeling and density functional theory (DFT) investigation for the interpretation of the adsorption of Paprika dye on TiO2 surface for dye sensitized solar cells. By using a statistical physics modeling method, an adequate monolayer model with four energies was successfully used to interpret the adsorption process at a macroscopic level. The DFT simulation has been used to study the interaction of the Paprika dye on TiO2 surface to understand some of the atomistic details that are crucial to the dye/semiconductor interaction. We pay particular attention to the adsorption modes, geometries and energies between the paprika dye and TiO2. The DFT simulation determined different binding modes which participated in the adsorption of Paprika dye on TiO2 surface: monodentate coordination via hydrogen atom bond, monodentate coordination via oxygen atom bond and bidentate coordination via two oxygen atoms bond. In particular, calculations showed that the interaction between the paprika dye and TiO2 is strengthened with the bidentate coordination mode via the two hydroxyl and ether functionalities groups involved in the adsorption process.

Statistical physics modeling of water vapor adsorption isotherm into kernels of dates: Experiments, microscopic interpretation and thermodynamic functions evaluation

In this paper, water sorption isotherms into date kernels give interesting insights about the sorption mechanism. The equilibrium adsorption data expressing the change in moisture content of date kernels were collected at three different temperatures using the static gravimetric technique. The adsorption isotherm profiles demonstrated that this process was performed via an infinite number of layers. A modified form of the Brunauer, Emett and Teller (BET) model is obtained based on the use of the real gas law and statistical physics treatment so the interaction between molecules is considered. This advanced model is used to fit experimental isotherms by numerical simulation. The sorption mechanism is theoretically explained by the parameters that could be related to the water adsorption process. Based on fitting results, we find that the number of molecules per site (parameter n) has a linear tendency with temperature thanks to the thermal agitation effect. A deeper analysis of adsorption energy demonstrates that the water vapors are physisorbed in the date kernels. Through the exploitation of our model, three classic thermodynamic functions are investigated to interpret the macroscopic aspect of the adsorption mechanism.

Adsorption of a non-steroidal anti-inflammatory drug onto MgAl/LDH-activated carbon composite – Experimental investigation and statistical physics modeling

A Layered Double Hydroxides (LDH) with Mg and Al composite (MgAl/LDH-biochar) was synthesised by the co-precipitation method, using bovine bone activated carbon as support structure for the LDH particles. The adsorbent was applied for diclofenac sodium (DS) removal from synthetic water. Batch experiments provided a DS removal of almost 80 % under optimized conditions. The performances of the MgAl/LDH-biochar composite (i.e. adsorption capacity as much as 5.96 mg/g) result significantly better when compared to the raw biochar (2.35 mg/g) at first 15 min. Despites the equilibrium data provided good adjustments for all tested models, Redlich-Peterson model showed the highest values of R2 and lower values of average relative error (ARE) and Akaike’s information criterion (AIC). The kinetic data of DS adsorption was best represented by the pseudo-second order model. The regenerability of MgAl/LDH-biochar was also evaluated through six adsorption/desorption cycles using either methanol or sodium chloride (0.5 mol/L) as desorbing agents, showing that the material can be reused until the third cycle maintaining a good adsorption capacity. The thermodynamic studies suggested that the adsorption process was spontaneous and exothermic, since the adsorption capacity decreased when the temperature increased. Finally, for a deeper insight in the DS adsorption mechanism, monolayer model formulated via statistical physics was adopted to describe the adsorption geometry of this relvant water pollutant and also to further characterize the interactions between DS and the tested adsorbent.

Statistical rock physics analysis and modelling in the Browse Basin

In this study, we performed rock physics analysis and modelling in the Browse Basin, in which we analysed the relationships among elastic properties of end-member (EM) sandstone (SST) and EM-shale,...

Statistical physics modeling and interpretation of the adsorption of dye remazol black B on natural and carbonized biomasses

Natural and carbonized pine-fruit shells (NPFS, and CPFS) were employed to study the adsorption of remazol black B dye (RBB) from aqueous solution. A theoretical analysis of the adsorption systems was performed via the statistical physics modeling of the experimental dye adsorption isotherms at 298–323 K and pH 3. Results showed that the adsorbent CPFS outperformed adsorbent NFPS for water decolorization. A multilayer advanced statistical physics model, which included monolayer and double layer adsorption scenarios, was employed to understand the RBB dye adsorption mechanism. Modeling analysis suggested that around two and three adsorbate layers were formed depending on the adsorption (i.e., adsorbent + dye RBB) systems at high temperature. The calculation of the linked dye molecules per leading adsorption site varied from 0.83 to 1.86 and from 1.10 to 2.88 for systems RBB-NPFS and RBB-CPFS, respectively. These results suggested that the dye RBB dye could be adsorbed on NPFS and CPFS surfaces via a non-horizontal orientation at tested operating conditions where the dye molecule aggregation phenomenon was present. Estimated adsorption energies confirmed an endothermic physisorption process for RBB dye removal. In summary, the statistical physics analysis provided a reliable interpretation of the adsorption mechanism of this textile pollutant on tested adsorbents.

Superparamagnetic Clustering of Diabetes Patients Raman Spectra

In this paper, we present a different way to the standard methods to classify Raman spectra whose grouping process is based on a phenomenon of clustering observed in nature at the atomic level and correctly described by the statistical physics model known as the Potts model, which represents the interacting spins on a crystalline lattice. This clustering method is known as the super paramagnetic clustering (SPC), which allows identifying hierarchical structures in data banks. In this novel method, we assigned a Potts spin to each data point (Raman spectrum) and introduced an interaction between neighboring points whose coupling strength is a decreasing function of the distance between the nearest neighboring sites. We found a hierarchical tree structure in our data bank of Raman spectra allowing us to discriminate between the spectra from control and diabetes patients. The sensitivity and specificity of the diabetes detection technique by Raman spectroscopy were calculated directly because the SPC method achieves an accurate determination of the members of each cluster. As a cross-check, SPC results were compared with published results of multivariate analysis, observing excellent agreements; however, the SPC method allows determining the members of all identified clusters explicitly.

GPU-Accelerated Simulation of Massive Spatial Data Based on the Modified Planar Rotator Model

A novel Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics has been recently introduced for efficient and automatic interpolation of big data sets, such as satellite and radar images. The MPR model does not rely on Gaussian assumptions. Spatial correlations are captured via nearest-neighbor interactions between transformed variables. This allows vectorization of the model which, along with an efficient hybrid Monte Carlo algorithm, leads to fast execution times that scale approximately linearly with system size. The present study takes advantage of the short-range nature of the interactions between the MPR variables to parallelize the algorithm on graphics processing units (GPUs) in the Compute Unified Device Architecture programming environment. It is shown that, for the processors employed, the GPU implementation can lead to impressive computational speedups, up to almost 500 times on large grids, compared to single-processor calculations. Consequently, massive data sets comprising millions of data points can be automatically processed in less than one second on an ordinary GPU.

Modeling of aircraft fuel consumption using machine learning algorithms

With the aid of recording systems such as the flight data recorder, information from aircraft sensors can be transmitted in-situ to airlines or maintenance providers during the flight in form of reports, or stored for subsequent analysis in the postprocessing. This allows the determination of current aircraft performance with regard to fuel consumption or emissions. At present, data in a highly aggregated form (predominantly averages) are used for statistical estimations or physical models. The metrics are calculated on a rolling basis as performance indicators of the aircraft and are then compared with book values from the manuals or with data from the performance monitoring system. However, this procedure represents only a situational, aggregated point evaluation of stable flight conditions. The data aggregation is based on strict validity limits for parameter variations. Furthermore, trigger conditions of the recording logic determine the number and quality of the transmitted reports, such, that only a few data points are available for performance analyses. To improve realistic performance analyses, the time series of all aircraft sensors over the entire flight mission (full-flight data) can be used. In contrast to physical models, this study presents data-based approaches using machine-learning tools from the field of artificial intelligence, to develop fuel flow models based on full-flight data. The proposed methods result in detailed statements for the diagnosis of aircraft fuel consumption. The paper deals with the model development and results of different analyses based on a variety of an airline’s operational flight data records. This study describes the learning methods and shows results for two different data-based models, including neural networks and decision trees. Finally, future applications for the models and an outlook on the authors’ activities will be provided.

Adsorption of dyes brilliant blue, sunset yellow and tartrazine from aqueous solution on chitosan: Analytical interpretation via multilayer statistical physics model

This study reports the statistical physics modeling of the adsorption of three dyes brilliant blue (BB), sunset yellow (SY) and tartrazine (TT) on chitosan from aqueous solution. A multilayer statistical physics model was applied to understand the dye adsorption at different temperatures (i.e., 298–328 K) and pH 3. Modeling results showed that the adsorption was performed with a horizontal position of BB, SY, and TT molecules on the chitosan surface. Dye adsorption capacities ranged from 406.19 to 814.27 mg/g for BB, from 924.88 to 1432.98 mg/g for SY and from 611.27 to 1065.55 mg/g for TT, respectively. Overall, the chitosan showed the highest adsorption capacities for dye SY (Q0 (SY-chitosan) > Q0 (TT- chitosan) > Q0 (BB- chitosan)). The analysis of adsorption energies indicated that the removal of these dyes was an exothermic physisorption process, which could be governed by steric parameters according to the results obtained with the multilayer statistical physics model. This study contributes with new theoretical and experimental findings of the dye adsorption using natural polymers.

Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes

AbstractWe study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models. We show that the logarithmic derivatives of the Fredholm determinants are directly related to solutions of the Painlevé II hierarchy. This confirms and generalizes a recent conjecture by Le Doussal, Majumdar, and Schehr [20]. In addition, we obtain asymptotics at $\pm \infty $ for the Painlevé transcendents and large gap asymptotics for the corresponding point processes.

Cr(VI) uptake by a new adsorbent of CTAB–modified carbonized coal: Experimental and advanced statistical physics studies

The interaction between cetyltrimethylammonium bromide (CTAB) and carbonized coal (CC) resulted in the fabrication of a novel adsorbent (CTAB/CC). The new composite was characterized and applied for hexavalent chromium Cr(VI) uptake at three temperatures (25, 35, and 45 °C) and solution pH 2.0. Based on the correlation coefficient (R2) and Chi–squared (χ2) values, Langmuir with maximum removal capacities of 78.67, 81.74, and 82.58 mg g−1 described adequately the attained experimental data at 25, 35, and 45 °C, respectively. Advanced statistical physics models were applied to better understand the interaction between Cr(VI) ions and CTAB/CC active sites. Steric, energetic and thermodynamics parameters for the satisfactory model (monolayer with two energies) were deeply interpreted. The active sites number (n) was in the range of 0.76 to 1.8 reflecting the presence of multi–docking and multi–ionic mechanisms in Cr(VI) adsorption onto CTAB/CC composite. By increasing temperature from 25 to 45 °C, the receptor sites density (NM) reduced from 45.83 to 22.76 mg g−1 for N1M, but improved from 22.23 to 55.01 mg g−1 for N2M (i.e., discordant behaviors). Energetically, the Cr(VI) adsorption onto the CTAB/CC adsorbent was endothermic and related to physical forces (i.e. <40 kJ mol−1). Adsorption capacities (Qsat1 and Qsat2) were enhanced with temperature, which confirmed the endothermic character of the removal processes. Steric and energetic parameters were involved in controlling the adsorption of Cr(VI) on CTAB/CC product. Thermodynamic parameters revealed the spontaneous nature and viability of Cr(VI) adsorption onto the CTAB/CC composite.

H2O2-activated anthracite impregnated with chitosan as a novel composite for Cr(VI) and methyl orange adsorption in single-compound and binary systems: Modeling and mechanism interpretation

A novel composite was prepared from chitosan and hydrogen peroxide–treated anthracite sheets and it was applied for the single and simultaneous adsorption of Cr(VI) and methyl orange (MO) at different temperature (25–45 °C) and pH (2–10). Experimental results showed that Cr(VI) as HCrO4− species was mainly removed by electrostatic interactions, while the reduced form Cr(III) was adsorbed via ion exchange and complexation reactions, thus concluding that Cr(VI) uptake was governed by adsorption–reduction coupled mechanism. Adsorption of MO on this composite was controlled by hydrogen bonding, n–π and also electrostatic attractions. Experimental data were fitted satisfactorily with Langmuir and Freundlich equations indicating that the composite was more selective for MO adsorption. Langmuir-based monolayer adsorption capacities (qmax) ranged from 188.01 to 201.77 mg/g for Cr (VI) and from 297.28 to 295.75 mg/g for MO in the single and binary systems, respectively, at 25 °C. Physicochemical parameters of statistical physics models were estimated and utilized to understand the adsorption mechanism of both adsorbates. A multi-docking and multi-molecular mechanisms could be present in the adsorption of Cr(VI) and MO, respectively. Density of receptor sites (NM) proved to be an essential factor that was associated to the adsorption capacities of the studied adsorbates and its values confirming the high selectivity of anthracite/chitosan active sites for MO uptake. The values of the adsorbed capacity ratio (Qb/Qs) revealed that MO enhanced uptake of Cr(VI) due to the newly formed active sites (i.e., synergism interaction), while MO adsorption was slightly decreased in the binary system at all temperatures reflecting a weak antagonism interaction. The adsorption energies corresponded to an exothermic process governed by physical forces for both pollutants.

A Multiset Version of Even-Odd Permutations Identity

In this paper, we present a multiset analogue of the even-odd permutations identity in the context of combinatorics of words. The multiset version is indeed equivalent to the coin arrangements lemma which is a key lemma in Sherman’s proof of Feynman’s conjecture about combinatorial solution of Ising model in statistical physics. Here, we give a bijective proof which is based on the standard factorization of a Lyndon word.

Adsorption of amoxicillin and tetracycline on activated carbon prepared from durian shell in single and binary systems: Experimental study and modeling analysis

The adsorption mechanism of two antibiotics, namely amoxicillin (AMX) and tetracycline (TCN), on durian shell activated carbon (AC) was investigated in single and binary systems. Adsorption isotherms were determined under the same experimental conditions and they showed that the adsorption capacities of AMX were higher than those of TCN at all tested temperatures suggesting that this adsorbent preferred to remove AMX from the aqueous solution. It was also observed that all adsorption capacities decreased from single to binary systems, which was reasonably explained by an antagonistic adsorption between AMX and TCN on the active sites of AC creating an inhibition effect between these adsorbates. Monolayer and competitive monolayer models were developed via statistical physics theory and they were applied to explain and understand the adsorption mechanism of AMX and TCN via steric and energetic parameters. Results suggested that the parallel and non-parallel orientations of both antibiotics on the adsorbent surface of AC could be possible at tested experimental conditions. Modeling results demonstrated that the numbers of accepted antibiotic molecules per active site of AC varied with linear and inverse trends in single and binary systems, respectively, at all tested temperatures thus corroborating the adsorption inhibition effect caused by both adsorbates. An estimation of adsorption energies was also performed to describe and characterize the interactions between both antibiotics and AC surface. The assessment of the parameters of statistical physics models contributed to the explanation of the single and binary adsorption mechanisms of these water pollutants.

Adsorption of crystal violet on biomasses from pecan nutshell, para chestnut husk, araucaria bark and palm cactus: Experimental study and theoretical modeling via monolayer and double layer statistical physics models

Biomasses from pecan nutshell (PN), para chestnut husk (PCH), araucaria bark (AB) and palm cactus (PC) were employed to study the adsorption mechanism of a relevant textile pollutant namely crystal violet (CV). Experimental isotherm data performed at the best condition of pH showed that the temperature had no effect on the adsorption of CV on PN and PCH, while the CV dye removal with AB and PC was significant affected by this operating parameter. Monolayer and double layer adsorption models were applied to analyze and explain, based on statistical physics, the removal mechanism of CV using these adsorbents. The application of these statistical physics models allowed to deduce theoretically that the active sites of PN and PCH practically attracted the same number (i.e., 1.12 < nms < 1.20) of CV dye molecules at all adsorption temperatures; while a variable number of CV dye molecules (0. 81 < nms < 2.10) could be bonded by the adsorption sites of adsorbents AB and PC. It was also confirmed that the temperature has a negligible effect on the adsorbed quantity of the systems CV-PN and CV-PCH, but it significantly impacted the systems CV-AB and CV-PC generating different magnitudes of the adsorption energies. The adsorption energy was calculated and the adsorption mechanism was analyzed thus suggesting that hydrogen bindings and van der Waals interactions could be possible for the adsorption of this dye on tested biomasses at optimum pH.

Algorithmic Pirogov–Sinai theory

We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\mathbb Z^d$ and on the torus $(\mathbb Z/n \mathbb Z)^d$. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-core model at sufficiently high fugacity on subsets of $\mathbb Z^d$ with appropriate boundary conditions and an efficient sampling algorithm for the ferromagnetic Potts model on the discrete torus $(\mathbb Z/n \mathbb Z)^d$ at sufficiently low temperature.

Statistical physics-based analysis of the adsorption of Cu2+ and Zn2+ onto synthetic cancrinite in single-compound and binary systems

Adsorption isotherms of Cu2+ and Zn2+ onto cancrinite were investigated in single-compound and binary systems at pH 6.0 and room temperature. The maximum adsorption capacity of Cu2+ was higher than Zn2+ in both the systems. This result could be related to Pauling electronegativity and hydrated ionic radius of these metals, making the cancrinite more selective for Cu2+ than Zn2. The separation factor (αCu,Zn) was greater than unity confirming the higher selectivity for Cu2+ adsorption. Langmuir and Freundlich models fitted well the single-compound adsorption isotherms. In order to obtain a better interpretation of the adsorption of Cu2+ and Zn2+ in single and binary systems, a monolayer and an exclusive extended monolayer models were adopted. According to these statistical physics models results, the receptor sites of cancrinite showed to be more selective for Cu2+ (n = 0.94) than Zn2+ (n = 0.77) in single-compound systems. Due to the competitive effect arising between Cu2+ and Zn2+ on the same receptor site, the n values were reduced in binary system to 0.68 and 0.39 for Cu2+ and Zn2+, respectively. Furthermore, the adsorption energies in single-compound systems were equal to 23.78 and 19.23 kJ/mol for Cu2+ and Zn2+, respectively. In binary system, the adsorption energies of the studied ions decreased and their values in all the systems indicated the existence of a physisorption process. The reduction of the adsorbed capacity ratio between the binary and single-compound systems (i.e. Qb/Qs) highlighted the antagonistic effect between copper and zinc ions. Finally, thermodynamic parameters were investigated in detail.

Evolution of protein interfaces in multimers and fibrils.

A majority of cellular proteins function as part of multimeric complexes of two or more subunits. Multimer formation requires interactions between protein surfaces that lead to closed structures, such as dimers and tetramers. If proteins interact in an open-ended way, uncontrolled growth of fibrils can occur, which is likely to be detrimental in most cases. We present a statistical physics model that allows aggregation of proteins as either closed dimers or open fibrils of all lengths. We use pairwise amino-acid contact energies to calculate the energies of interacting protein surfaces. The probabilities of all possible aggregate configurations can be calculated for any given sequence of surface amino acids. We link the statistical physics model to a population genetics model that describes the evolution of the surface residues. When proteins evolve neutrally, without selection for or against multimer formation, we find that a majority of proteins remain as monomers at moderate concentrations, but strong dimer-forming or fibril-forming sequences are also possible. If selection is applied in favor of dimers or in favor of fibrils, then it is easy to select either dimer-forming or fibril-forming sequences. It is also possible to select for oriented fibrils with protein subunits all aligned in the same direction. We measure the propensities of amino acids to occur at interfaces relative to noninteracting surfaces and show that the propensities in our model are strongly correlated with those that have been measured in real protein structures. We also show that there are significant differences between amino acid frequencies at isologous and heterologous interfaces in our model, and we observe that similar effects occur in real protein structures.

Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation

The analysis of various models in statistical physics relies on the existence of decompositions of measures into mixtures of product-like components, where the goal is to attain a decomposition into measures whose entropy is close to that of the original measure, yet with small correlations between coordinates. We prove a related general result: For every measure $$\mu $$ on $${\mathbb {R}}^n$$ and every $$\varepsilon > 0$$ , there exists a decomposition $$\mu = \int \mu _\theta d m(\theta )$$ such that $$H(\mu ) - {\mathbb {E}}_{\theta \sim m} H(\mu _\theta ) \le \mathrm {Tr}(\mathrm {Cov}(\mu )) \varepsilon $$ and $${\mathbb {E}}_{\theta \sim m} \mathrm {Cov}(\mu _\theta ) \preceq \mathrm {Id}/\varepsilon $$ . As an application, we derive a general bound for the mean-field approximation of Ising and Potts models, which is in a sense dimension free, in both continuous and discrete settings. In particular, for an Ising model on $$\{\pm \, 1 \}^n$$ or on $$[-\,1,1]^n$$ , we show that the deficit between the mean-field approximation and the free energy is at most $$C \frac{1+p}{p} \left( n\Vert J\Vert _{S_p} \right) ^{\frac{p}{1+p}} $$ for all $$p>0$$ , where $$\Vert J\Vert _{S_p}$$ denotes the Schatten-p norm of the interaction matrix. For the case $$p=2$$ , this recovers the result of Jain et al. (Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective. arXiv:1808.07226 , 2018), but for an optimal choice of p it often allows to get almost dimension-free bounds.

Adsorption of indium (III) from aqueous solution on raw, ultrasound- and supercritical-modified chitin: Experimental and theoretical analysis

The adsorption of indium (III) on raw, supercritical- and ultrasound-modified chitin was experimentally and theoretically studied. Experimental adsorption data demonstrated that the profile of all adsorption isotherms was different from a system to another. Indeed, the adsorption behavior of the systems indium (III) – chitin and indium (III) – supercritical-modified chitin tended to a saturation process at high concentration thus suggesting that the adsorption can be occurred by the formation of a fixed number of adsorbate layers. Contrary to this finding, the adsorption of indium (III) on an ultrasound-modified chitin can be associated to a variable number of layers involving two adsorption energies. Statistical physics models were selected to understand the adsorption data and they demonstrated that the adsorption of indium (III) – chitin and indium (III) – supercritical-modified chitin was achieved by the formation of one layer; while the adsorption of this adsorbate on an ultrasound-modified chitin was performed with a variable number of layers. Based on the modeling analysis, it was demonstrated that the ultrasonic treatment improved the properties of chitin to remove this pollutant: Qesat of ultrasound-modified chitin > Qesat of supercritical-modified chitin > Qesat of raw chitin. The interpretation of parameter n, which is defined as a number of bonded ions of indium (III) per responsible site of the adsorbent, was higher than 1 at high temperature. This result suggested that the indium adsorption was a multi-ionic mechanism. All adsorption systems were characterized by an estimation of the adsorption energy reflecting that the removal of this pollutant involved physical interactions. A general analysis of all model parameters indicated that the receptor site density and the adsorption energy controlled the indium adsorption.