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We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing model. The main tool used in this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and digital options, or backward random processes. In the last case, the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end, we discuss the paradox involving the drift parameter $$\mu $$ μ in the Black–Scholes–Merton model pricing. We provide sensitivity analysis and an approximation of the speed of convergence for the asymptotically vanishing effect of drift in prices.

A simple theory of thermodynamic properties of liquid nitrogen solution in Fe–Mn alloys is proposed. This theory is completely analogous to the theory for liquid nitrogen solution in alloys of the Fe–Cr system proposed previously by the authors in 2019. The theory is based on the lattice model of the considered Fe–Mn solutions. The model assumes a FCC lattice. The atoms of Fe and Mn are in these lattice sites. Nitrogen atoms are located in octahedral interstices. The nitrogen atom interacts only with the metal atoms located in the lattice sites neighboring to it. This interaction is pairwise and it is assumed that the energy of this interaction depends neither on the composition nor on the temperature. Furthermore, the solution in the Fe–Mn system is assumed to be perfect. Within the framework of the proposed theory, a relation was obtained that expresses the value of the Sieverts law constant for N solubility in liquid Mn through the similar constant for the N solubility in liquid Fe and the Wagner N–Mn interaction coefficient in liquid Fe. The values of the Sieverts law constants in this relation are taken directly from the experimental measurements of the solubility of N in liquid Fe and in liquid Mn. In this case, the obtained relation is considered as an equation with respect to the Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ . The equation’s solution gives the value of Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ = –5.25 in liquid steel at a temperature of 1873 K. Wagner interaction coefficient $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ is related with Langenberg interaction coefficient $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ by the relation deduced by Lupis and Elliott in 1965. The relation includes the atomic masses of Fe and Mn. By substituting the value $$\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}$$ = –5.25 and solving the resulting equation with respect to $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ , we obtain the value $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ = –0.0230. This value corresponds to the experimental data of Beer (1961), which is likely one of the most probable of all experimental values of $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ for liquid steel at 1873 K. Another such value is $$e_{{\text{N}}}^{{{\text{Mn}}}}$$ = 0.0209 obtained by Shin with coworkers in 2011.

The effect of residual secondary structures in peptides and proteins on their separation is considered within the framework of the lattice model of adsorption and chromatography of macromolecules. It is shown that, if the model takes into account secondary structures, such as helices, folds, or crosslinks, the retention volume may change considerably. At the same time, for short peptides with the number of amino-acid units on the order of 20, which result from the enzymatic hydrolysis of proteins, the effect of secondary structures, for example, residual S–S crosslinks, on separation in the model chromatographic experiment is insignificant. For such peptides the main effect on seраration is exerted by their amino-acid composition, and the values of retention volume may be adequately predicted both under the linear chain approximation and in terms of the adsorption additivity model.

Surfactant-induced Marangoni flows can alter the typical outward capillary flows in a drying droplet. Previous studies show that intricate time-dependent periodic motions of colloidal particles, such as Marangoni eddies and back-and-forth oscillatory motions, can be developed due to the coupled dynamics of surfactant and evaporation. Here, the temporal motions are investigated using a coarse-grained lattice model. We show that during the evaporation, aggregation and depletion zones of colloidal particles emerge close to the contact line when the capillary and Marangoni flows are comparable in the opposite directions. It is found that the type of periodic motions is determined by the initial surfactant concentration. When the strength of the Marangoni flows is sufficiently large at the early stage of evaporation swirling motions rather than oscillatory motions are developed. The periodic motions of particles persist until the surfactant concentration on the surface is saturated. Also, the onset and terminate times of the motions decrease with the initial surfactant concentration.

First-principles calculations and a model consideration of magnetically frustrated layered material PdCrO2 are performed. The results on the exchange parameters are in agreement with the experimental data on the Curie-Weiss temperature (θ). We show that experimentally observed strong suppression of the Néel temperature (TN) in comparison with the Curie-Weiss temperature is due to three main factors. First, as expected, this is connected with the layered structure and relatively small exchange interaction along the c axis. Second, deformation of the ideal in-plane 120° magnetic structure is crucial to provide finite TN value. However, these two factors are still insufficient to explain low TN and the large frustration factor |θ|/TN. Thus, we suggest a scenario of an exotic non-Fermi-liquid state in PdCrO2 above TN within the frameworks of the Anderson lattice model, which seems to explain qualitatively all its main peculiarities. © 2020 American Physical Society. Authors are grateful to Yu. N. Skryabin for useful discussions. This research was carried out within the state assignment of FASO of Russia via program Quantum (No. AAAA-A18-118020190095-4). We also acknowledge support by Russian Ministry of Science via Contract No. 02.A03.21.0006. Calculations were performed using the Supercomputing Center of IMM UrB RAS. The work of M.I.K. is supported by European Research Council via Synergy Grant No. 854843–FASTCORR.

We develop a binomial lattice model of zero-leverage behaviour using a real option on debt issuance. With the option, firms may delay issuance even when debt is feasible and adds value to the firm....

A molecular dynamic experiment is carried out for analyzing the isotherms of adsorption on a graphene surface at temperatures below and above the critical values for adsorptives. It is shown that the monomolecular isotherms of gas adsorption on the flat carbon surfaces can be described using the set of equations of the lattice model and the equations of the theory of the volume filling of micropores (TVFM). The obtained results are compared with the experimental data on adsorption in micropores of active carbons. When describing the isotherms of polymolecular adsorption with the use of the BET and the Aranovich equations, the filling of each layer is analyzed.

Accurate characterization of methane absolute adsorption in shale nanoporous media is of great importance to the gas-in-place (GIP) estimation and well productivity. Because experimental measurement can only provide the excess adsorption, the absolute adsorption is generally converted from the excess adsorption based on the single-layer adsorption model. However, it is well known that shale has a widespread pore size distribution (PSD), ranging from sub 2-nm to hundreds of nanometers. In micropores ( Based on the varying density profiles in different nanopores obtained from GCMC, we propose the corresponding methane adsorption model in each nanopore, which is applied in Ono-Kondo (OK) lattice model. By fitting the excess adsorption in nanoporous media and explicitly considering the PSD, OK model can readily obtain the absolute adsorption. In order to validate our model, 1000 sets of randomly generated PSDs are used. We find that our proposed OK model has an excellent agreement with GCMC simulation, while the commonly used method to convert the excess adsorption to the absolute adsorption without considering the PSD shows noticeable deviations. Moreover, the optimized constant adsorbed phase densities are very different from the commonly used values as 424 kg/m3 and 373 kg/m3. Our work proposes a simple, efficient and accurate empirical model to obtain the absolute adsorption in nanoporous media. This work should provide important insights into accurate characterization methane absolute adsorption and the gas-in-place estimation in shale.

The Kovacs effect is a remarkable feature of the ageing dynamics of glass forming liquids near the glass transition temperature. It consists in a non-monotonous evolution of the volume/enthalpy after a succession of two abrupt temperature changes: first from a high initial temperature $T_i$ to a much lower annealing temperature $T_a$ followed by a smaller second jump back to a slightly higher final temperature $T_f$. The second change is performed when the instantaneous value of the volume/enthalpy coincides with the equilibrium one at the final temperature. While this protocol might be expected to yield equilibrium dynamics right after the second temperature change, one observes the so-called Kovacs hump in glassy systems. In this paper we apply such thermal protocol to the Distinguishable Particles Lattice Model (DPLM) for a wide range of fragility of the system. We study the Kovacs hump based on energy relaxation and all main experimental features are captured. Results are compared to general predictions based on a master equation approach in the linear response limit. We trace the origin of the Kovacs hump to the non-equilibrium nature of the probability distribution of particle interaction energies after the annealing and find that its difference with respect to the final equilibrium distribution is non-vanishing with two isolated zeros. This allows Kovacs' condition of equilibrium total energy to be met out-of-equilibrium, thus representing the memory content of the system. Furthermore, the hump is taller and occurs at a larger overlap with the system initial configuration for more fragile systems. The dynamics of a structural temperature for the mobile regions strongly depends on the glass fragility while for the immobile ones only a weak dependence is found., Comment: 9 pages, 9 figures: Added fragility study and encoding of the memory in the particles interaction energy distribution; added doi

Nanoscale metal-organic frameworks (nMOFs) have recently been shown to provide better radiosensitization than solid nanoparticles when excited with X-rays. Here we report the first Monte Carlo simulation of different radiosensitization effects by nanoparticles and nMOFs using a lattice model consisting of 3D arrays of nanoscale secondary building units (SBUs). The simulation results reveal that lattices outperform solid nanoparticles regardless of radiation sources or particle sizes via enhanced scatterings of photons and electrons within the lattices. Optimum dose enhancement can be achieved by tuning SBU size and inter-SBU distance.

We study properties of thermal transport and quantum many-body chaos in a lattice model with $N\to\infty$ oscillators per site, coupled by strong anharmonic terms. We first consider a model with only optical phonons. We find that the thermal diffusivity $D_{\rm th}$ and chaos diffusivity $D_L$ (defined as $D_L = v_B^2/ \lambda_L$, where $v_B$ and $\lambda_L$ are the butterfly velocity and the scrambling rate, respectively) satisfy $D_{\rm th} \approx \gamma D_L$ with $\gamma\gtrsim 1$. At intermediate temperatures, the model exhibits a "quantum phonon fluid" regime, where both diffusivities satisfy $D^{-1} \propto T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $\hbar/k_B T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstone's theorem. As a result, for $d=1,2$, we find that $D_{\rm th}/D_L\to \infty$, while for $d=3$, $D_{\rm th}$ and $D_{L}$ remain comparable., Comment: 16 + 9 pages, 8 + 1 figures, updated version to match published version

Synaptic receptor and scaffold molecules self-assemble into membrane protein domains, which play an important role in signal transmission across chemical synapses. Experiment and theory have shown that the formation of receptor-scaffold domains of the characteristic size observed in nerve cells can be understood from the receptor and scaffold reaction and diffusion processes suggested by experiments. We employ here kinetic Monte Carlo (KMC) simulations to explore the self-assembly of synaptic receptor-scaffold domains in a stochastic lattice model of receptor and scaffold reaction-diffusion dynamics. For reaction and diffusion rates within the ranges of values suggested by experiments we find, in agreement with previous mean-field calculations, self-assembly of receptor-scaffold domains of a size similar to that observed in experiments. Comparisons between the results of our KMC simulations and mean-field solutions suggest that the intrinsic noise associated with receptor and scaffold reaction and diffusion processes accelerates the self-assembly of receptor-scaffold domains, and confers increased robustness to domain formation. In agreement with experimental observations, our KMC simulations yield a prevalence of scaffolds over receptors in receptor-scaffold domains. Our KMC simulations show that receptor and scaffold reaction-diffusion dynamics can inherently give rise to plasticity in the overall properties of receptor-scaffold domains, which may be utilized by nerve cells to regulate the receptor number at chemical synapses.

The self-assembly of amyloidogenic peptides and proteins into fibrillar structures has been intensively studied for several decades, because it seems to be associated with a number of neurodegenerative diseases, such as Alzheimer’s and Parkinson’s disease. Therefore, understanding the molecular mechanisms of this phenomenon is important for identifying an effective therapy for the corresponding diseases. Protein aggregation in living organisms very often takes place on surfaces like membranes and the impact of a surface on this process depends not only on the surface chemistry but also on its topology. Our goal was to develop a simple lattice model for studying the role of surface roughness in the aggregation kinetics of polypeptide chains and the morphology of aggregates. We showed that, consistent with the experiment, an increase in roughness slows down the fibril formation, and this process becomes inhibited at a very highly level of roughness. We predicted a subtle catalytic effect that a slightly rough surface promotes the self-assembly of polypeptide chains but does not delay it. This effect occurs when the interaction between the surface and polypeptide chains is moderate and can be explained by taking into account the competition between energy and entropy factors.

Non-enzymatic polymerisation explained how life could assemble spontaneously on the early Earth. Prior research has discovered that the non-enzymatic polymerisation can be mediated by various environmental settings, most widely accepted are the reactions driven by the cycles of hydration and dehydration and organising matrices such as clay, salt, membranes and mineral surface. Membranes have a unique feature which prepares it as a sensitive organising matrix, as compared to mineral surface and clay, which transforms its phase with small changes in temperature, hydration and composition of lipids. Multi-component membranes can show phase separation where two or more distinct phases can co-exist. To the best of our knowledge, this is for the fi?rst time the influence of different phases of the membrane in the nucleotide organisation and polymerisation in a simulated prebiotic setting in this work have been explored. This study encompasses the energetics of inserting a mononucleotide, UMP, in distinct membrane settings which is probed utilising the PMF. The preferential partitioning of UMP is also investigated; which is coupled to the location of the insertion and the composition of the PSM/DOPC/Chol membranes. Combined with umbrella-sampling calculations, AA-MD simulations were performed to estimate the role of themonophasic and diphasic membrane in modifying the behaviour of UMPs and their clustering mechanism. A mathematical model was also developed based on lattice model and random walk and some of the parameters were trained from the AA-MD simulations. The results indicated that the membranes were capable of concentrating nucleotides and organised into anisotropic clusters, and the thermodynamic studies along with mathematical model showed that it had a sharp preference for the Lo/Ld domain interface for clustering.

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

This work examined the effect of macrostep height on the growth velocity of a vicinal surface during reaction- (interface-) limited crystal growth under non-equilibrium steady state conditions. The Monte Carlo method was employed, based on a restricted solid-on-solid (RSOS) model with point-contact-type step-step attraction (termed the p-RSOS model). Although this is a simple lattice model, the model surface shows a variety of distinctive configurations depending on the temperature and the driving force for crystal growth. The results demonstrate that the surface velocity decreases as the height of the faceted macrostep increases. In addition, the significant variation in surface velocity recently reported by Onuma {\it et al.} in a study based on 4H-SiC was reproduced. This work also shows that the terrace slope, elementary step velocity and elementary step kinetic coefficient are all affected by the faceted macrostep height., 11pages, 12 figures. This manuscript was prepared for the achesmo (a latex package for the ACS). Since the achesmo is not supported, this manuscript was converted to RevTeX. This manuscript is submitted to the Crystal Growth & Design

Accurate characterization of shale gas adsorption capacity is of great importance to the gas-in-place estimation and prediction of well productivity. Propane is one of major constituents in shale gases which can have multilayer adsorption behavior on pore surfaces. While experiments can measure excess adsorption, the absolute adsorption, which describes adsorbed gas capacity, has to be converted from the excess adsorption. In previous works, absolute adsorption is usually calculated from excess adsorption with adsorbed phase volume or density based on the single-layer adsorption model. However, for heavier alkanes, such as ethane and propane, which can have multilayer adsorption behavior, single-layer adsorption model becomes invalid. While molecular simulation can characterize the multilayer adsorption behavior, it comes with expensive computational costs. Currently, there is no viable model to characterize the absolute adsorption of hydrocarbons which can have multilayer adsorption behavior. In this work, we conduct grand canonical Monte Carlo (GCMC) simulation to study propane adsorption in shale nanopores over a wide range of pressures at temperature higher than the critical temperature. We find that propane can form multiple adsorption layers, thus, using single-layer adsorption model to obtain the absolute adsorption becomes unjustifiable. Based on the propane density distribution characteristics, we propose a multilayer adsorption model and use Ono-Kondo (OK) lattice model with multilayer structures to regress propane excess adsorption and subsequently obtain the absolute adsorption in each layer. For propane, we take into account the correlation effect arising from strong adsorbate–adsorbate interactions beyond mean field theory (MFT) and the only predetermined parameters are number of layers and adsorption layer width. The proposed OK model shows an excellent agreement with GCMC simulations on the excess adsorption and absolute adsorption in each layer, with discrepancies less than 6% above 50 bar. The proposed OK model can readily take into account the propane multilayer adsorption behavior, while significantly reducing calculation time. Our method presents a reliable and highly-efficient approach for accurate characterization of adsorption of hydrocarbons with multilayer structures and provide important insights into the gas-in-place estimation in shale.

We study quasi-equilibrium migration of double stranded DNA (dsDNA) through semi-circular narrow channel by exact enumeration method. We employ Fokker–Planck formalism to analyze the slow migration process of dsDNA through this symmetric channel which resembles the herpes simplex virus -1 (HSV-1) migration through the vestibular nuclei in brainstem. We explore all possibilities of varying solvent gradient inside the semi circular area to ensure slow migration which is essential in DNA nanopore sequencing techniques. We also shed light on configurational and orientational properties of DNA and sequential preference of the dsDNA while migrating through the channel. We report that GC rich homo-sequence DNA migrates more slowly through the channel than AT rich and AT-GC di-block DNA. In this paper, a simple lattice model is developed to explore various physical parameters dependence on slow migration process of a dsDNA.

The classical pore structure conceptual model, such as a bundle of capillaries and lattice model is challenged for applicability in unconventional reservoirs, due to the micro/nano pore scale in unconventional reservoirs, with most of them below 100nm. Meanwhile, it is important to obtain an accurate evaluation of imbibition efficiency in unconventional reservoirs since imbibition is the main method for sweeping oil in matrix. This paper improves the acyclic pore model which is more practical for unconventional reservoirs. An imbibition efficiency calculation method is proposed, the effects of bifurcation number, pore throat radii corresponding to a mercury saturation of 50% (r50) and wettability is studied. The mechanism about how the pore structure affects imbibition performance is revealed. Results show that the increment of bifurcation number can decelerate the imbibition time in the branch level with smaller diameter, enlarges the imbibition accessible pore size as well. As r50 and hydrophilic saturation increase, wetting fluid volume imbibed and driving force for imbibition is also enhanced, which results in an improvement of imbibition efficiency.

ESR measurements of [CLPOT-(4-X-TEMPO)] inclusion compounds (CLPOT = 2,4,6-tris(4-chlorophenoxy)-1,3,5-triazine, and 4-X-TEMPO = 4-substituted-2,2,6,6-tetramethyl-1-piperidinyloxyl radical) with 1D organic-radical molecular chains constructed in organic 1D nanochannels used as templates were conducted in the range of temperatures from 4.2 to 300 K. The peak-to-peak line width (ΔBpp) of all isotropic ESR spectra of the [CLPOT-(4-X-TEMPO)] was much narrower in the whole temperature range than the estimation based on the Van Vleck’s formula for the second moment of the rigid lattice model. In addition, the line profiles of all ESR spectra of the [CLPOT-(4-X-TEMPO)] became Lorentzian in the whole temperature range, compared with our previous results using tris(o-phenylenedioxy)cyclotriphosphazene (TPP) as templates in which the ESR profiles were temperature-dependent. These results indicate that the narrower ESR line width of the [CLPOT-(4-X-TEMPO)] may be caused not by motional narrowing but by 3D exchange i...

The segmental dynamics and the corresponding glass temperature, Tg, were investigated in a monocyclic and in the corresponding linear polystyrene as well as in a series of multicyclic polystyrenes, all with the same total molecular weight, with dielectric spectroscopy and DSC. There is a strong reduction of Tg with decreasing molecular weight for linear chains but only a moderate reduction for cyclic chains and this below a certain critical molecular weight (Mn ∼ 18 000 g/mol). These data contradict the Gibbs–Di Marzio lattice model predicting an increasing glass temperature with decreasing molecular weight of cyclic polymers. In multicyclic polystyrenes the results emphasize the role of constrained segments at the coupling sites (linkers) on determining practically all features of segmental dynamics: the exact temperature dependence of relaxation times and associated Tg, the dielectric strength, the distribution of relaxation times, and fragility. A nearly linear increase of Tg was found with increasing ...

We construct a discrete-time option valuation model capable of taking into consideration multiple exercises and stochastic interests rates under a generalized Brennan–Rubinstein framework, and further apply the Geske and Johnson (1984) method for the valuation of American options. For implementation, we use only the once- and twice-exercisable option values to approximate American option values. Our numerical results show that the effects of stochastic interest rates are very large, particularly for out-of-the-money American put options with a high-risk underlying asset price. For options with a high-risk return on asset as the underlying assets, the effects of stochastic interest rates are negligible, even for options with long-term maturity. Finally, the sign of correlation between asset prices and bond prices plays an important role in determining whether the values of American put options under stochastic interest rates are larger or smaller than those under constant interest rates.

Here we focus on the conformational search for the native structure when it is ruled by the hydrophobic effect and steric specificities coming from amino acids. Our main tool of investigation is a 3D lattice model provided by a ten-letter alphabet, the stereochemical model. This minimalist model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. We have three central goals here. The first one is to characterize the folding time ( τ ) by two distinct sampling methods, so we present two sets of 103 MC simulations for a fast protein-like sequence. The resulting sets of characteristic folding times, τ and τ q were obtained by the application of the standard Metropolis algorithm (MA), as well as by an enhanced algorithm ( M q A ). The finding for τ q shows two things: (i) the chain-solvent hydrophobic interactions { h k } plus a set of inter-residues steric constraints { c i , j } are able to emulate the conformational search for the native structure. For each one of the 1 0 3 MC performed simulations, the target is always found within a finite time window; (ii) the ratio τ q ∕ τ ≅ 1 ∕ 10 suggests that the effect of local thermal fluctuations, encompassed by the Tsallis weight, provides to the chain an innate efficiency to escape from energetic and steric traps. We performed additional MC simulations with variations of our design rule to attest this first result, both algorithms the MA and the M q A were applied to a restricted set of targets, a physical insight is provided. Our second finding was obtained by a set of 600 independent MC simulations, only performed with the M q A applied to an extended set of 200 representative targets, our native structures. The results show how structural patterns should modulate τ q , which cover four orders of magnitude; this finding is our second goal. The third, and last result, was obtained with a special kind of simulation performed with the purpose to explore a possible connection between the hydrophobic component of protein stability and the native structural topology. We simulated those same 200 targets again with the M q A , only. However, this time we evaluated the relative frequency { ϕ q } in which each target visits its corresponding native structure along an appropriate simulation time. Due to the presence of the hydrophobic effect in our approach we obtained a strong correlation between the stability and the folding rate ( R = 0 . 85 ). So, as faster a sequence found its target, as larger is the hydrophobic component of its stability. The strong correlation fulfills our last goal. This final finding suggests that the hydrophobic effect could not be a general stabilizing factor for proteins.

The method of entropic sampling within the Wang–Landau algorithm (a modern variant of the Monte Carlo method) is used to determine the densities of energy states of a strongly charged star-shaped polyelectrolyte within the framework of the lattice model. The equilibrium thermal and structural properties of the polyelectrolyte with the number of arms f ≤ 6 and the length of arms N arm ≤ 73 in a wide temperature range are determined from the density of states. Such characteristics as the free energy, the mean-squared radius of gyration, its components, and the parameters characterizing the shape of a polyion are calculated. It is found that the concentration, length, and number of arms affect the thermal and structural properties. The main attention is focused on the effect of temperature on these properties. The coil-to-globule transition is detected, while for the polyion with the highest length of arms (N arm = 24) the transition from the liquid globule to the crystal-like one is observed. Differences in the properties of the star-shaped and corresponding linear polyions are characterized.

Single-layer $h\ensuremath{-}\mathrm{BN}$ is known to have edges with unique magnetism; however, in the commonly fabricated multilayer ${\text{AA}}^{\ensuremath{'}}\ensuremath{-}h\ensuremath{-}\mathrm{BN}$, edge relaxations occur that create interlayer bonds and eliminate the unpaired electrons at the edge. Recently, a robust method of growing the unconventional Bernal-stacked $h\ensuremath{-}\mathrm{BN}$ ($\mathrm{AB}\ensuremath{-}h\ensuremath{-}\mathrm{BN}$) has been reported. Here, we use theoretical approaches to investigate the nitrogen-terminated zigzag edges in $\mathrm{AB}\ensuremath{-}h\ensuremath{-}\mathrm{BN}$ that can be formed in a controlled fashion using a high-energy electron beam. We find that these ``open'' edges remain intact in bilayer and multilayer $\mathrm{AB}\ensuremath{-}h\ensuremath{-}\mathrm{BN}$, enabling researchers potentially to investigate these edge states experimentally. We also investigate the thermodynamics of the spin configurations at the edge by constructing a lattice model that is based on parameters extracted from a set of first-principles calculations. We find that the edge spins in neighboring layers interact very weakly, resulting in a sequence of independent spin chains in multilayer samples. By solving this model using Monte Carlo simulations, we can determine nm-scale correlation lengths at liquid-${\mathrm{N}}_{2}$ temperatures and lower. At low temperatures, these edges may be utilized in magnetoresistance and spintronics applications.

In this paper we study the electrostatic attraction between two parallel rodlike DNA polyelectrolytes induced by neutralizing multivalent counterions at the zero temperature limit. The counterions crystallize on the charged surfaces of DNA so that we can handle the system by using the Wigner crystal lattice model. We derived the 3D ground state configuration of counterions with minimized energy by use of the gradient descent method, and calculated the interaction between two DNA cylinders with divalent or trivalent counterions when they approach. The results show that the complex ground state configuration of counterions plays a key role in determining the caused attraction. The counterions form three-dimensional Wigner crystals on each cylinder at large separation. When the cylinders are brought together, some counterion lines will move towards the inner region and lead to strong attraction. The calculated interaction from our model is in good agreement with the simulation result, however, the single particle approximation considerably overestimates the attraction.

Molecular self-assembly is usually done at low supersaturation, leading to low rates of growth, in order to allow time for binding mistakes to anneal. However, such conditions can lead to prohibitively long assembly times where growth proceeds by the slow nucleation of successive layers. Here we use a lattice model of molecular self-assembly to show that growth in this regime can be sped up by impurities, which lower the free-energy cost of layer nucleation. Under certain conditions impurities behave almost as a catalyst in that they are present at high concentration at the surface of the assembling structure, but at low concentration in the bulk of the assembled structure. Extrapolation of our numerics using simple analytic arguments suggests that this mechanism can reduce growth times by orders of magnitude in parameter regimes applicable to molecular systems.

A water/oil/amphiphilic polymer ternary system is analyzed by Monte Carlo (MC) method using a lattice model to determine the thermal equilibrium distribution by changing the component ratio. Particularly the rheological properties such as shear stress and viscosity are evaluated via Monte Carlo Brownian Dynamics (MCBD) simulation, in which the flexibility of polymer movement is considered by the bond fluctuation model and the shear force is expressed by the Kramers potential. Our analysis on the micelle pattern for each concentration ratio shows that, the increase of polymer concentration decreases the solute (water, polymer) mobility, and exponentially increases the viscosity. These results in our simulation reflect general phenomena in concentrated colloid system. By assuming that the polymer orientation dominates the stress of system by the elasticity between polymer bonds, we newly find that from the polymer placement under the shear field, the shear stress itself exponentially increases while raising the concentration. Even in the category of lattice model, our study indicates the possibility of acquiring new knowledge on Dynamics by using a polymer model with specific consideration on flexible mobility and MCBD method.

Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random “cloud-like” configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the “cloud-like” morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity’s distribution characteristics, such as area fraction, shape, and relative location on the casting’s equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations: (1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%; (2) the average Stress Concentration Factor (SCF) produced by shrinkage porosity is about 2.0; (3) the defect’s length across the loading direction plays a more important role in the effective modulus than the length along the loading direction; (4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

A Monte Carlo lattice model is proposed to describe the formation of semiconductor nanostructures by the vapor–liquid–solid growth mechanism. This model is used to simulate the growth of GaAs nanostructures by the droplet epitaxy technique in the temperature range from 500 to 600 K in As2 fluxes with intensity of 0.005–0.04 ML/s. The morphology of the formed structures is demonstrated to depend on the growth parameters. Etching of the GaAs substrate by a gallium droplet is studied. The ranges of temperature and As flux rates necessary for the formation of GaAs nanorings are determined. The conditions of the formation of single and double concentric rings are analyzed.

Cation disorder is a phenomenon that is becoming increasingly important for the design of high-energy lithium transition metal oxide cathodes (LiMO2) for Li-ion batteries. Disordered Li-excess rocksalts have recently been shown to achieve high reversible capacity, while in operando cation disorder has been observed in a large class of ordered compounds. The voltage slope (dVdxLi) is a critical quantity for the design of cation-disordered rocksalts, as it controls the Li capacity accessible at voltages below the stability limit of the electrolyte (∼4.5–4.7 V). In this study, we develop a lattice model based on first principles to understand and quantify the voltage slope of cation-disordered LiMO2. We show that cation disorder increases the voltage slope of Li transition metal oxides by creating a statistical distribution of transition metal environments around Li sites, as well as by allowing Li occupation of high-voltage tetrahedral sites. We further demonstrate that the voltage slope increase upon disor...

We studied the structural order in randomly perturbed nematic liquid crystals using a random anisotropic nematic-type lattice model. Simulations were carried out at zero temperature and at various other temperatures, for which we varied the concentration of impurities p, anchoring strength W and imposed external strength fields B at two different histories: temperature-quenched history (TQH) and field-quenched history. The Haller approximation method utilized the temperature dependence of the order parameter to determine the pseudo-critical exponent β at different values of p and W. Consequently, the values of β increased when p and W were increased. Additionally, applying an external field B for investigating the parameters revealed that the TQH established long-range order for high magnitudes of B at zero temperature (T* = 0) and T* = 0.5.

Adsorption of a single homopolymer chain with bending stiffness on a homogeneous planar surface is studied theoretically in the framework of the lattice model and the generating functions approach. The stiffness is introduced by assigning a statistical weight to a trans-isomer (a straight segment) with respect to a gauche-isomer (a kink). This statistical weight is related to the bending energy e b e n d associated with a kink: k = exp ( e b e n d ∕ k B T ) and depends on the temperature but one can also treat k as a temperature-independent parameter. Both positive and negative values of the bending energy corresponding to stiff ( e b e n d > 0 , k > 1 , positive stiffness) and “quasi-zigzag” ( e b e n d 0 , 0 k 1 , negative stiffness) chains are considered. The dependence of the adsorption transition temperature on e b e n d and k is non-monotonic and has a minimum for flexible chains at e b e n d = 0 and k = 1 . At the same time, at moderate and strong adsorption, the fraction of adsorbed units is a strictly increasing function of the bending energy or the stiffness parameter. Adsorption is accompanied by the straightening of the chain in the case of positive e b e n d and its “zigzaging” in the case of negative e b e n d . In contrast, when k is temperature independent, a decrease in temperature leads to the increase in the fraction trans-isomers at any positive k . The temperature dependence of the specific heat can exhibit one or two maxima in addition to the jump in at the adsorption (second order) transition point.

Fuel assembly bowing is a known phenomenon observed in many PWR reactors all over the world. The phenomenon is relevant to safety as it can lead to increased water gaps between assemblies which results in higher pin peaking factors. The goal of the present study is to assess the effect of assembly bowing not only for stead-state nominal conditions but also during a transient. The selected transient is the loss of one reactor coolant pump as it can be limiting especially regarding the Departure from Nucleate Boiling (DNB) safety criterion. This study focuses on an extreme case where the bowing is simulated in the core hot assembly by keeping the water gap constant over the whole core active length. The resulting cross-sections and form functions obtained from a 2d infinite lattice model are used in the nodal diffusion code DYN3D applying its pin-by-pin reconstruction method. For the transient simulation, DYN3D is coupled with the thermal-hydraulics subchannel code CTF on the SALOME platform. Several modelling options are compared: nominal geometry for neutronics and thermal-hydraulics (TH); mixed: neutronics with increased water gap, TH with nominal geometry; and increased water gap for both neutronics and TH. The results confirm that the increased water gap should be considered in both models in order to reduce the conservatism.

For disordered catalysts such as atomically dispersed "single-atom" metals on amorphous silica, the active sites inherit different properties from their quenched-disordered local environments. The observed kinetics are site-averages, typically dominated by a small fraction of highly active sites. Standard sampling methods require expensive ab initio calculations at an intractable number of sites to converge on the site-averaged kinetics. We present a new method that efficiently estimates the site-averaged turnover frequency (TOF). The new estimator uses the same importance learning algorithm [Vandervelden et al., React. Chem. Eng. 5, 77 (2020)] that we previously used to compute the site-averaged activation energy. We demonstrate the method by computing the site-averaged TOF for a simple disordered lattice model of an amorphous catalyst. The results show that with the importance learning algorithm, the site-averaged TOF and activation energy can now be obtained concurrently with orders of magnitude reduction in required ab initio calculations.

The precipitation of a glass forming solute from solution is modelled using a lattice model previously introduced to study dissolution kinetics of amorphous materials. The model includes the enhancement of kinetics at the surface of a glass in contact with a plasticizing solvent. We demonstrate that precipitation can produce a glass substantially more stable than that produced by very long time annealing of the bulk glass former. The energy of these ultra-stable amorphous precipitates is found to be dominated by residual solvent rather than high energy glass configurations.

The majority of proteins perform their cellular function after folding into a specific and stable native structure. Additionally, for many proteins less compact ‘molten globule’ states have been observed. Current experimental observations show that the molten globule state can show varying degrees of compactness and solvent accessibility; the underlying molecular cause for this variation is not well understood. While the specificity of protein folding can be studied using protein lattice models, current design procedures for these models tend to generate sequences without molten globule-like behaviour. Here we alter the design process so the distance between the molten globule ensemble and the native structure can be steered; this allows us to design protein sequences with a wide range of folding pathways, and sequences with well-defined heat-induced molten globules. Simulating these sequences we find that (1) molten globule states are compact, but have less specific configurations compared to the folded state, (2) the nature of the molten globule state is highly sequence dependent, (3) both two-state and multi-state folding proteins may show heat-induced molten globule states, as observed in heat capacity curves. The varying nature of the molten globules and typical heat capacity curves associated with the transitions closely resemble experimental observations.

Self-assembly of a two-component mixture of trimesic acid (TMA) and 1,3,5-benzene-tribenzoic acid (BTB) was studied by a Monte Carlo calculation. To describe the ordering, the three-state lattice model with homo- and heteromolecular dimeric and trimeric interactions was proposed. We also took advantage of the same symmetry and size effect of TMA and BTB molecules. The molecular interactions between TMA and BTB molecules were calculated by the density functional theory. Our simulations reproduced the self-assembly of all pure and bicomponent phases of TMA and BTB previously found in the experiments. Several new mixed structures were predicted at TMA:BTB ratios of 2:1, 1:1, and 1:2. The conditions of TMA and BTB phase intermixing and coexistence were also clarified by the ground state analysis. The simplest hypothetical structures which might occur due to the mixed trimeric interactions were studied, and their formation conditions were determined.

One of the most notable deviations from bulk fluid properties is the onset of a thickness-dependent glass transition temperature (Tg) for nanometrically thin polymer films. Experimental and theoretical observations suggest that this behavior is a response to the interfaces, which perturb the local properties of a film and play an increasingly important role in influencing the global properties of a film as its thickness decreases. In this work, we probe the global and local properties of free-standing films using our limited mobility (LM) model, which is a simple kinetic lattice model that simulates free volume and mobility in a fluid. We provide insight about the role of mobility in affecting the thickness-dependent film-average Tg of free-standing polymer films by characterizing the depth to which mobility propagates from a free surface, i.e., the “mobile layer depth”. We also consider the effect of “stacking” free-standing polymer films, where confinement by interfaces composed of the same material yie...

In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM.

We present a detailed Monte Carlo study of the effects of molecular biaxiality on the defect created at the centre of a nematic droplet with radial anchoring at the surface. We have studied a lattice model based on a dispersive potential for biaxial mesogens [Luckhurst et al., Mol. Phys. 30, 1345 (1975)] to investigate how increasing the biaxiality influences the molecular organisation inside the confined system. The results are compared with those obtained from a continuum theory approach. We find from both approaches that the defect core size increases by increasing the molecular biaxiality, hinting at a non universal behaviour previously not reported.

Discretized virtual internal bond (DVIB) is a lattice model, which is composed of bond cells. Each bond cell has a finite number of bonds. The DVIB is used to model the creep fracture. It is done by introducing a viscous bond to the original hyperelastic DVIB. The hyperelastic bond is parallel coupled with a viscous bond together, forming a hybrid hyperelastic-Kelvin bond. The hyperelastic bond reflects the microfracture mechanism, whereas the viscous bond reflects the creep mechanism. Based on this hyperelastic-Kelvin bond, the constitutive relation of a cell is derived. The microbond parameters are calibrated based on the ideal cell approach. The simulation results suggest that this method can represent the typical features of creep and can simulate the creep fracture. The merit of this method lies in that the complicated 3D macrocreep problem is reduced to the 1D microbond creep problem. No creep law is previously derived. The macrocreep fracture behavior is the natural response of the assembly of the micro hyperelastic-Kelvin bonds.

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite ($+-$ scenario) or identical ($++$ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the {\it same} winding number emerge under appropriate distortion (interaction, etc), following the $++$ scenario. Under further distortion, these Dirac points merge following the $+-$ scenario, that is corresponding to {\it opposite} winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general., Comment: 5 pages, 6 figures

Atomistic simulations based on the static lattice model are performed to calculate the equilibrium and growth morphologies of CdS polymorphs. Morphologically important surfaces are optimized to calculate their structural and energetical properties such as surface and attachment energies. A common feature of all the nonpolar CdS surfaces is the outward movement of their anions and the inward movement of their cations. The relaxation of surfaces is critically important as it changes the surface and attachment energies significantly. The {1120} surface has the lowest surface energy (0.58 J/m2) for the wurtzite phase of CdS, whereas {110} surface has the lowest surface energy (0.62 J/m2) for the zincblend phase of CdS. The {1010}, {1230}, and {1100} surfaces of wurtzite CdS all have the same surface energy value (0.60 J/m2), which is very close to that of {1120} surface. Therefore, all these surfaces appear in the equilibrium morphology of the wurtzite CdS. The equilibrium morphology of the zincblend CdS...

Copyright © 2015 Published by Elsevier B.V. Torsten Hägerstrand’s 1953 study of innovation diffusion [1] was pathbreaking in many ways. It was based on an explicit micro-model of information spread, and on Monte Carlo simulation of the hypothesised spatial process. Using the original aggregated data and Hope-type tests of the ability of the simulations to capture the observed adoptions, (author?) [2] and (author?) [3] and others found problems. This study attempts to examine the extent to which we may be able to "do better" with a range of approaches drawn from spatial statistics, including using a SAR lattice model, geostatistical modelling, Moran eigenvectors, and other approaches.

The driving force dependence of the surface velocity and the average height of faceted merged steps, the terrace-surface-slope, and the elementary step velocity in the non-equilibrium steady-state are studied using the Monte Carlo method. The Monte Carlo study is based on a lattice model, the restricted solid-on-solid model with point-contact type step--step attraction (p-RSOS model). The temperature is selected to be in the step-faceting zone where the surface is surrounded by the (001) terrace and the (111) faceted step at equilibrium. Long time simulations are performed at this temperature to obtain steady-states for the different driving forces that influence the growth/recession of the surface. A Wulff figure of the p-RSOS model is produced through the anomalous surface tension calculated using the density-matrix renormalization group method. Although the p-RSOS model is a simplified model, the model shows a wide variety of dynamics in the step-faceting zone. There are four characteristic driving forces, $\Delta \mu_y$, $\Delta \mu_f$, $\Delta \mu_{co}$, and $\Delta \mu_R$. For $\Delta \mu_{co}, Comment: 16 pages, 13 figures

A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with a small rate $\alpha$, and interact via exclusion volume only. When increasing the tumbling rates $\alpha$, the system transits from total wetting to partial wetting and unwetting phases. In the first phase, a wetting film covers the wall, with increasing heights when $\alpha$ is reduced. The second phase is characterized by wetting droplets on the wall with a periodic spacing between them. Finally, the wall dries with few particles in contact with it. These phases present nonequilibrium transitions. The first transition, from partial to total wetting, is continuous and the fraction of dry sites vanishes continuously when decreasing the tumbling rate $\alpha$. For the second transition, from partial wetting to dry, the mean droplet distance diverges logarithmically when approaching the critical tumbling rate, with saturation due to finite-size effects.

We report quantum chemical calculations to address yet unresolved and puzzling questions regarding the structural and magnetic disorder of V[TCNE] x (TCNE = tetracyanoethylene, x ∼ 2), the first room-temperature molecule-based magnet. Starting from an ideal lattice model, containing TCNE ligands either tetra- or bi-connected to vanadium(II) ions, we identify the key sources of structural disorder, explaining the amorphousness and non-stoichiometric nature of V[TCNE] x . The proposed model is prone to static disorder in terms of the bulk distribution of the tetra-connected TCNE species and to dynamic effects due to the relative rotational freedom of the bi-connected TCNE moieties. Density functional theory (DFT) calculations of the model system with rotated TCNE molecules show a rough energy landscape, consistent with the presence of magnetic irreversibilities in the system. The broken symmetry DFT approach evidences ferrimagnetic spin orientation for all TCNE configurations, ruling out the spin glass model. Multiconfigurational calculations with additional spin–orbit interaction allow for the account of the single-ion-anisotropy of the V(II) ions in different environments. We determine a small uniform zero-field-splitting ( D c = −0.03 K) of the bulk as well as a sizeable random anisotropy ( D r = 0.56 K) due to TCNE vacancies. We clarify the interplay of ferrimagnetism and random magnetic anisotropy in this system, which favours correlated sperimagnetic and not spin glass behaviour, in agreement with puzzling experimental data. Our approach goes beyond the material of interest here, as it can be applied to other disordered molecular magnets by correlating the sources of disorder with their effects on the magnetic properties.

A recent scheme for calculating approximate vibrational mode lifetimes in solids (Dickel and Daw, 2010) [1,2] is extended to the next level (fourth-moment). The extension is tested in two cases: (1) simple, low-dimensional anharmonic systems, and (2) on a simple lattice model of vibrations. We show that, for systems where the mode-resolved density of states is well-approximated by a single broadened peak, the fourth-moment approximation works well over a wide range of temperatures.

We present an original Probabilistic Monte Carlo (PMC) model for pricing European discrete barrier options and compound real options. On the basis of Monte Carlo (MC) simulation, for barrier options the PMC model computes the probability of not crossing the barrier for knock-out options and crossing the barrier for knock-in options. This probability is then multiplied by an average sample discounted payoff of a plain vanilla option that has the same inputs as the barrier option but barrier-free, and to which we have applied a filter. We test the consistency of our model with an analytical solution (Merton, 1973; Reiner and Rubinstein, 1991) adjusted for discretization by Broadie et al (1997) and a naive numerical model using MC simulation presented by Clewlow and Strickland (2000). Our study shows that the PMC model accurately prices barrier options. Moreover, the idea behind the method is simple and can be applied to the pricing of complex derivatives, easing the valuation step significantly: we illustrate the versatility of the PMC model in pricing sequential compound real options. Market participants needing to select a reliable, versatile and simple numerical method for pricing options with embedded features will find our article appealing.