Statistical Physics Models Research Articles

Synergistic adsorption of Pb2+ and CrO42− on an engineered biochar highlighted by statistical physical modeling

Statistical physics-based adsorption models were used to provide a deep analysis of the single and binary adsorption of Pb2+ and CrO42− on an engineered biochar. New physical interpretations of the adsorption mechanisms of these pollutants were reported. Results showed that the adsorption capacities in binary systems were higher than those obtained in single systems at 298 K. The adsorption capacities at saturation were 606 and 346 mg/g for Pb2+ and CrO42− in mono-component systems, while they were 1420 and 488 mg/g for these pollutants in binary solutions at 298 K. Model parameters confirmed the presence of a synergistic adsorption effect between both ions (Pb2+ and CrO42−) on the same functional group of the biochar. Modeling results allowed to sketch the adsorption orientation of metallic adsorbates on the adsorbent surface and to estimate the corresponding adsorption energies. These calculations indicated an endothermic adsorption due to the presence of both physical and chemical interactions in the single and binary adsorption systems. Overall, both steric and energetic factors affect the adsorption mechanisms of Pb2+ and CrO42−on this novel biochar.

Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes.

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

A recyclable multifunctional graphene oxide/SiO2@polyaniline microspheres composite for Cu(II) and Cr(VI) decontamination from wastewater

Recently, the discharge of metal ions into the aquatic environments has become the main issue because of its role in the ecological system pollution. Herein, a recyclable multifunctional graphene oxide/silica@polyaniline (GO/SiO2@PANI) microspheres composite was synthesized, characterized, and tested for Cu(II) and Cr(VI) ions uptake. The interaction between the studied ions and GO/SiO2@PANI composite was rapid, and the optimum pH values were 5.3 for Cu(II) while pH 3.0 for Cr(VI). The Cu(II)) and Cr(VI) adsorption data at equilibrium reflected proper corrections for traditional Langmuir and Freundlich equations at 30, 40, and 50 °C. Fourier-transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) analysis revealed that the Cu(II) adsorption onto GO/SiO2@PANI function groups was mainly governed by electrostatic force. Hexavalent chromium was removed in the form of HCrO4−via electrostatic interaction and Cr(III) by the ion exchange. The geometry of the removed ions on the GO/SiO2@PANI receptor sites was deeply interpreted using advanced statistical physics models (ASPM). Single and two-layer with dual-energy sites fitted perfectly with Cr(VI) as well as Cu(II) sorption data. Horizontal and vertical directions were presented in Cr(VI) uptake, indicating the presence of adsorption–reduction coupled mechanism. For Cu(II) ions, only the horizontal position was distinguished, reflecting the participation of various receptor sites of the GO/SiO2@PANI in the removal of copper ion. The adsorption energies for both metals ions were below 40 kJ/mol signifying an endothermic process governed by physical interactions. Removal of both ions in the binary system and regeneration process indicated that the GO/SiO2@PANI composite is a promising adsorbent for metals-bearing water.

Adsorptive removal of sunset yellow dye by biopolymers functionalized with (3–aminopropyltriethoxysilane): Analytical investigation via advanced model

The adsorption of dye sunset yellow (SY) on both raw and functionalized chitosan (CTN and CTNF) was investigated using statistical physics theory. Adsorption data of SY dye on CTN and CTN-F were experimentally obtained at 298–328 K. Statistical physics modeling analysis demonstrated that the adsorption capacities at 298–328 K of both systems were similar. This theoretical evidence explained that the functionalization of the raw chitosan via 3-aminopropyltriethoxysilane did not improve the adsorbent performance. It was also concluded that the SY dye interacted via the same orientation on CTN and CTNF. The effect of the temperature on the adsorption capacity was studied and results indicated that the SY dye adsorption on CTN and CTN-F adsorbents was endothermic. Dye adsorption capacities were due to the similarity in the number of the attracted SY dye molecules per adsorption site and the density of this receptor site. The interactions between SY dye and adsorbents (CTN and CTNF) and also between SY dye molecules were understood via the calculation of adsorption energies. Physical interactions were the responsible of the dye adsorption mechanism using adsorbents CTN and CTN-F.

Stochastic Channel Access in Underwater Networks With Statistical Interference Modeling

Designing efficient medium access control protocols for underwater acoustic sensor networks (UW-ASNs) is a major challenge because of the spatial and temporal interference uncertainty caused by asynchronous transmissions and by the low propagation speed of sound. To address these challenges, in this article we propose a new approach for distributed underwater medium access based on lightweight and asynchronous distributed algorithms that optimize the access probability profile over a series of time slots based on a new statistical physical interference model. The latter is based on measuring the level of interference at multiple instants of time in each time slot in order to capture the effects of temporal uncertainty and of unaligned interference. At each measurement instant, the statistical properties of time-varying interference are represented by a Gamma probability distribution. The model is validated through extensive channel measurement experiments conducted with an underwater acoustic testbed in Lake LaSalle. Based on this model, we formulate the problem of queue-aware stochastic channel access. The objective is to maximize the sum throughput of a set of concurrent and mutually interfering source-destination pairs by letting the transmitters adjust their own transmission probability profiles, without collaborating with each other, over a series of time slots based on a statistical characterization of interference obtained through past observations. We propose an iterative distributed solution algorithm for this problem based on a best-response strategy. At each iteration, each node individually solves a non-convex optimization problem of logarithmic complexity. The performance of the proposed distributed algorithm is evaluated by comparing it with two alternative distributed schemes and with the global optimum obtained through a newly-developed centralized globally optimal solution algorithm. Results indicate that by jointly taking the queueing and multi-slot optimization into consideration considerable improvement in terms of sum-throughput can be achieved by the proposed distributed algorithm.

A novel experimental technique for the fabrication of the vitamin B12 nucleus using quartz crystal microbalance: Statistical physics modeling and new microscopic properties

A novel adsorption model for the description of adsorption isotherms of cobalt nitrate on porphyrins H2TPP and H2TTPP is developed in the present paper. Experimental data were measured at five temperatures using the quartz crystal microbalance technique and were discussed to choose the most reproductive adsorbent for the achievement of the vitamin B12 nucleus. Then, the modeling treatment was established based on the grand canonical formalism in statistical physics by taking into account the lateral interaction between the adsorbate particles. This leads to a six parameter equation describing the complexation process at the molecular level. Actually, there is a good correlation between experimental data and those calculated by using the double-layer L.B.L. model. It was found that cobalt ions were adsorbed via a multi-docking mechanism onto the two adsorbents. The study of the density of receptor sites (PM) confirmed the endothermic nature of the two complexation processes. The van der Waals parameters indicated that the disturbances following the lateral interactions between the adsorbates are the highest in the case of tetraphenylporphyrin. The magnitude of the calculated adsorption energies reveals that cobalt is physisorbed onto tetraphenylporphyrin, whereas chemical forces were found in the case of porphyrins (H2TTPP). In addition, the proposed model allows the prediction of some adsorption thermodynamic functions, which govern the adsorption mechanism, such as entropy, Gibbs free enthalpy, and internal energy.

Event-by-event neutron–photon multiplicity correlations in [formula omitted]Cf(sf)

Excited nuclear fragments are emitted during nuclear fission. The de-excitation of these fission fragments takes place as sequential emission of neutrons followed by photons. Correlations between neutron and photon multiplicities accompanying fission is thus expected. Fission event generators based on established statistical nuclear physics models predict negative event-by-event correlations in neutron–photon multiplicity. A survey of published experimental results of an event-by-event covariance between the neutron and photon multiplicities emitted following the spontaneous fission of 252Cf is presented. Analytic unfolding expressions are developed in this work to determine the bias introduced by background sources, particle misclassification, pulse pileup, and inelastic photon production. The published experimental data are re-analyzed using these unfolding techniques and are found to be in qualitative agreement with the predictions of model-based calculations. In particular, we have concluded that there exists a significant event-by-event neutron–photon emission competition following the spontaneous fission of 252Cf.

Insights of the adsorption mechanism of methylene blue on brazilian berries seeds: Experiments, phenomenological modelling and DFT calculations

The adsorption of the methylene blue on the biomass obtained from brazilian berries seeds was studied. Experimental adsorption data and results of the physicochemical characterization of the adsorbent besides theoretical physics-based calculations were utilized to understand the dye adsorption mechanism. A monolayer adsorption model was proposed to simulate the dye adsorption assuming an interaction adsorbent + adsorbate via two different functional groups on biomass surface. This statistical physics model calculated the number of bonded MB dye molecules and the saturated adsorption capacity for both functional groups at different temperatures. For instance, the values of n1 and n2 were 0.34 and 0.51 at 298 K thus indicating that MB molecules interacted via a horizontal adsorption orientation with two and three functional groups of biomass surface. Calculations based on statistical physics and density functional theory characterized the role and relevance of proposed functional groups on dye adsorption including its thermodynamic parameters. Results demonstrated that the hydrogen and oxygen functionalities of biomass surface were the main responsible functional groups for dye adsorption. Therefore, this paper reports new findings to understand the adsorption mechanism of dye molecules on lignocellulosic biomasses.

Statistical analysis and stochastic interest rate modeling for valuing the future with implications in climate change mitigation

High future discounting rates favor inaction on present expending while lower rates advise for a more immediate political action. A possible approach to this key issue in global economy is to take historical time series for nominal interest rates and inflation, and to construct then real interest rates and finally obtaining the resulting discount rate according to a specific stochastic model. Extended periods of negative real interest rates, in which inflation dominates over nominal rates, are commonly observed, occurring in many epochs and in all countries. This feature leads us to choose a well-known model in statistical physics, the Ornstein–Uhlenbeck model, as a basic dynamical tool in which real interest rates randomly fluctuate and can become negative, even if they tend to revert to a positive mean value. By covering 14 countries over hundreds of years we suggest different scenarios and include an error analysis in order to consider the impact of statistical uncertainty in our results. We find that only 4 of the countries have positive long-run discount rates while the other ten countries have negative rates. Even if one rejects the countries where hyperinflation has occurred, our results support the need to consider low discounting rates. The results provided by these fourteen countries significantly increase the priority of confronting global actions such as climate change mitigation. We finally extend the analysis by first allowing for fluctuations of the mean level in the Ornstein–Uhlenbeck model and secondly by considering modified versions of the Feller and lognormal models. In both cases, results remain basically unchanged thus demonstrating the robustness of the results presented.

Dipyridyl-based organo-silica nanosheets for three emerging micropollutants efficient removal: Adsorption performance and mechanisms

Dipyridyl-based organo-SiNSs (DHBP-SiNSs) was prepared by combining silica nanosheets (SiNSs) with dipyridyl-containing gemini surfactant (DHBP) and employed as adsorbent to effectively remove three emerging pharmaceuticals and personal care products (PPCPs) (Clofibric acid (CA), Ketoprofen (KP) and Naproxen Sodium (NPX)). Key characteristic analysis of DHBP-SiNSs, such as interlayer spacing, surfactant arrangement and the stacking unit of platelets was conducted. The influences of pH, contact time and concentration of the adsorbates were investigated in detail. The results suggested the effective retention of CA (216.59 mg/g), KP (326.36 mg/g) and NPX (260.57 mg/g) at a short time and DHBP-SiNSs can be regenerated at least for 3 cycles. Kinetics, isotherms and thermodynamic parameters were studied to reveal the adsorption mechanism. Based on the comparison of n-octanol-water partition coefficient (Kow) and organic-matter-corrected sorption coefficient (Kom), fitting of statistical physics models and characterizations of spent samples, the structure-adsorption relationships were explained. The adsorption of NPX was governed by π-π interaction, however, partition and π-π stacking were the dominant mechanisms for KP. Multiple interactions (e.g. partition, OH-π interaction, π-π interaction and π-π stacking) were responsible for the efficient elimination of CA. Differentiations of the adsorption process verified that (i) the strength of π-π interaction: pyridine/naphthalene > pyridine/benzene > pyridine/orthogonally benzene, (ii) the strength of π-π stacking: orthogonally benzene > benzene > naphthalene, (iii) π-π interaction between pyridine/naphthalene > the synergy of OH-π interaction between hydroxyl/pyridine and π-π interaction between pyridine/benzene. This study not only enlarged the application of organo-SiNSs as effective adsorbents but also threw more lights on the structure-adsorptive capacity relationships.

Adsorption of methylene blue on comminuted raw avocado seeds: Interpretation of the effect of salts via physical monolayer model

In this work, the effect of salts on the adsorption of a textile pollutant (Methylene blue: MB) on comminuted raw avocado seeds (CRAS) was interpreted via a physical monolayer model (PMM). To this aim, ten MB adsorption isotherms were determined at 25 °C and pH 10 in the presence of the next salts: NaCl, Na 2 CO 3 , Na 2 SO 3 , NaHCO 3, C 6 H 5 Na 3 O 7 , NaHSO 3, Na 2 B 4 O 7 ·10H 2 O, Na 2 S 2 O 3, NaNO 2 and Na 2 HPO 4 . Under the same experimental conditions, a further adsorption isotherm was also determined without any salt addition and taken as reference data. In order to achieve a theoretical interpretation of the experimental data and to address the effect of salts on adsorption mechanism, a physical monolayer model (PMM) was applied to all the retrieved data. The model showed that Na 2 CO 3 , NaHCO 3 , Na 2 B 4 O 7 , Na 2 S 2 O 3 , and NaNO 2 salts have no effect on the adsorption of MB dye, while the presence of NaCl, Na 2 SO 3 , C 6 H 5 Na 3 O 7 , NaHSO 3 and Na 2 HPO 4 salts in the solution caused a slight decrement of MB adsorption capacity due to a competitive effect between MB dye and salts on CRAS adsorption site. The modeling analysis showed that MB was adsorbed with a mixed parallel and non-parallel orientation on CRAS adsorbent surface. Moreover, the adsorption energies varied from 19.44 to 22.36 kJ/mol in tested systems. Adsorption energy values revealed that the process evolved via a physical adsorption, regardless the salt present in solution. All the investigated salts did not functionalize the CRAS adsorbent surface and also did not change the interaction energy between MB molecules and the adsorbent receptor sites. The interpretation of all the model parameters contributed to explain the adsorption mechanism of MB dye on CRAS. Specifically, the effect of salt on the reduction of MB adsorption capacity seems to be likely due to both steric hindrance effect and to MB molecule aggregation hindrance exerted by the salts, which prevented the formation of subsequent MB adsorbed layers, thus limiting its overall adsorption capacity. • MB dye adsorption mechanism was analyzed via statistical physical modeling. • Salts effect on dye adsorption on a lignocellulosic biomass was performed. • Description of the adsorption mechanism through an energetic factor.

Mathematical modeling for flocking flight of autonomous multi-UAV system, including environmental factors

In this study, we propose a decentralized mathematical model for predictive control of a system of multi-autonomous unmanned aerial vehicles (UAVs), also known as drones. Being decentralized and autonomous implies that all members make their own decisions and fly depending on the dynamic information received from other unmanned aircraft in the area. We consider a variety of realistic characteristics, including time delay and communication locality. For this flocking flight, we do not possess control for central data processing or control over each UAV, as each UAV runs its collision avoidance algorithm by itself. The main contribution of this work is a mathematical model for stable group flight even in adverse weather conditions (e.g., heavy wind, rain, etc.) by adding Gaussian noise. Two of our proposed variance control algorithms are presented in this work. One is based on a simple biological imitation from statistical physical modeling, which mimics animal group behavior; the other is an algorithm for cooperatively tracking an object, which aligns the velocities of neighboring agents corresponding to each other. We demonstrate the stability of the control algorithm and its applicability in autonomous multi-drone systems using numerical simulations.

Adsorption of hazardous dyes on functionalized multiwalled carbon nanotubes in single and binary systems: Experimental study and physicochemical interpretation of the adsorption mechanism

The crystal violet (CV) and rhodamine B (RhB) dyes were selected in this paper to study their adsorption on functionalized multiwalled carbon nanotubes (MCN). Adsorbent morphology and its corresponding physicochemical properties were characterized by applying various experimental techniques namely SEM, XRD and FTIR. Results of phenomenological modeling and the experimental adsorption data showed that the adsorption capacities of both dyes in single solutions were similar. However, synergistic and antagonistic adsorption effects were observed in binary solutions. Results indicated that the CV dye molecule was practically adsorbed in a double amount in comparison to the RhB dye molecule at most of the adsorption temperatures. Saturation adsorption capacities ranged from 0.57 to 0.86 mmol/g and from 0.75 to 0.88 mmol/g for CV and RB dyes at 298–328 K, respectively. It has been concluded that the size of dye molecule played a negligible role during the adsorption. CV and RhB dye molecules can interact with the same functional groups of the adsorbent. A competitive statistical physics model was reliable to predict the multicomponent adsorption behavior of these dyes. The adsorption orientation of both dyes was discussed using the results of the physical modeling and a possible theoretical mechanism was proposed based on the estimated adsorption energies. Finally, the effect of temperature on the adsorbent performance for both single and binary dye solutions was analyzed providing a clear understanding of the observed trends in the experimental dye adsorption capacities.

Phase space classification of an Ising cellular automaton: The Q2R model

An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the so-called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them –which we call of type S-I, S-II, and S-III– share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 × 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation.

Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: Experiments, characterization and physical interpretations

Activated carbons were prepared from ashitaba waste and a walnut shell to study the adsorption mechanism of congo red and methylene blue dyes in aqueous solution. These adsorbents were characterized via XRD, FTIR and SEM techniques and the dye adsorption isotherms at three temperatures were quantified. A statistical physics model was applied to interpret the adsorption mechanism of tested dyes and adsorbents. Modeling results showed that these dyes were practically separated in the solution leading to an absence of the aggregation process. Adsorption orientations of dye molecules on the adsorbents changed depending on the temperature and nature of systems. The adsorption capacity of ashitaba waste activated carbon for the removal of congo red was significant thus indicating strong interactions between this dye and tested adsorbent. Calculated adsorption energy varied from 7.25 to 20.43 kJ/mol and they showed that the adsorption of both adsorbates occurred via physical interactions at different temperatures where the removal process was endothermic.

Transition in relaxation paths in allosteric molecules: Enzymatic kinetically constrained model

A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also incorporates enzymatic reactions to extend the classic model for allosteric regulation. Through Monte Carlo simulations, we found that the relaxation dynamics are much slower than the elementary reactions and are logarithmic in time with several plateaus, as is commonly observed for glasses. This is because of the kinetic constraints from the cooperativity via the competition for an enzyme, which has different affinity for molecules with different structures. Our model showed symmetry breaking in the relaxation trajectories that led to inherently kinetic transitions without any correspondence to the equilibrium state. In this paper, we discuss the relevance of these results for diverse responses in biology.

New insights in the physicochemical investigation of the vitamin B12 nucleus using statistical physics treatment: interpretation of experiments and surface properties.

In this research paper, the equilibrium isotherms for the adsorption of cobalt(ii)nitrate and cobalt(ii)chloride on tetrakis(4-tolylphenyl)porphyrin (H2TTPP) were obtained at four temperatures for modeling analysis. The experimental data describing the adsorbed quantity of cobalt particles were measured using the quartz crystal microbalance (QCM) strategy. Then, statistical physics formalism was employed to interpret the complexation mechanism by applying the real gas law that contemplates the interaction between the adsorbate particles in the free state. Advanced models treated with the law of van der Waals were applied for the single and L.B.L adsorptions of Co2+ at various temperatures (288–318 K). The experimental adsorption data of CoCl2 on porphyrins were satisfactorily fitted with the monolayer equation, showing that the chlorine particles had no effect on the complexation system, while the nitrate particles were involved in the adsorption of Co(NO3)2 and contributed to the layer formation. The physicochemical parameters of statistical physics models were estimated and used to compare the complexation mechanisms of both adsorbates. The study of the cohesion pressure (a) and the co-volume (b) confirmed that cobalt chloride guaranteed more stability during the formation of the vitamin B12 nucleus. Deeper energetic analysis demonstrated that cobalt ions were complexed by ionic or covalent bonds in the case of cobalt chloride (complexation energy (–E1/2) varies from −48.2 to −50.3), while a physisorption process took place in the case of cobalt nitrate ((–E1) varies from −33.6 to −36.1), thus indicating that CoCl2–H2TTPP was the most stable complex. The statistical physics models were also used to investigate two thermodynamic functions that govern the adsorption mechanisms, namely, the configurational entropy and the Gibbs free enthalpy.

An Entropy Analysis of Classroom Conditions Based on Mathematical Social Science

In classroom management, it is well-known that students’ mental states are strongly related to classroom conditions. There are many ways to describe human behavior in mathematical modeling in sociology. In social science, a model to describe human behavior has been developed by an analogy with the ferromagnetic spin model in statistical physics. Entropy, on the other hand, can express the order and/or disorder in many-body systems. The concept of entropy can be extended to continuous random variables in the information theory, which is called “differential entropy” and has been a powerful tool in many stochastic systems. Here, we show that classroom conditions can be expressed by the differential entropy, based on the model used in social science. To assess the applicability of this method to real classroom conditions, we investigated fluctuations in students’ minds with pictures and a questionnaire relating to school life, and then applied this to the present method, and calculated the differential entropy. The results correspond well with real classroom conditions, and suggest the usefulness of the present method. The significance of the present research is the proposal of a new method which has not yet been used in educational psychology.

Adsorption of Methane on Shale: Statistical Physics Model and Site Energy Distribution Studies

Adsorption behaviors of methane on four Sichuan Basin shales at different temperatures (318, 338, and 358 K) were experimentally investigated. The adsorption equilibrium data were best fitted by us...

An energy model for recognizing the prokaryotic promoters based on molecular structure

Promoter is an important functional elements of DNA sequences, which is in charge of gene transcription initiation. Recognizing promoter have important help for understanding the relative life phenomena. Based on the concept that promoter is mainly determined by its sequence and structure, a novel statistical physics model for predicting promoter in Escherichia coli K-12 is proposed. The total energies of DNA local structure of sequence segments in the three benchmark promoter sequence datasets, the sole prediction parameter, are calculated by using principles from statistical physics and information theory. The better results are obtained. And a web-server PhysMPrePro for predicting promoter is established at http://202.207.14.87:8032/bioinformation/PhysMPrePro/index.asp, so that other scientists can easily get their desired results by our web-server.