Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.

Spontaneous nucleation of structural defects in inhomogeneous ion chains

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble-Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg-Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.

Localized structures in complex plasmas in the presence of a magnetic field

In this work, the general framework in which fits our investigation is that of modeling the dynamics of dust grains therein dusty plasma (complex plasma) in the presence of electromagnetic fields. The generalized discrete complex Ginzburg-Landau equation (DCGLE) is thus obtained to model discrete dynamical structure in dusty plasma with Epstein friction. In the collisionless limit, the equation reduces to the modified discrete nonlinear Schrödinger equation (MDNLSE). The modulational instability phenomenon is studied and we present the criterion of instability in both cases and it is shown that high values of damping extend the instability region. Equations thus obtained highlight the presence of soliton-like excitation in dusty plasma. We studied the generation of soliton in a dusty plasma taking in account the effects of interaction between dust grains and theirs neighbours. Numerical simulations are carried out to show the validity of analytical approach.

Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e. g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

Thickness-induced stabilization of ferroelectricity in SrRuO3/Ba0.5Sr0.5TiO3/Au thin film capacitors

Pulsed-laser deposition has been used to fabricate Au/Ba0.5Sr0.5TiO3/SrRuO3/MgO thin film capacitor structures. Crystallographic and microstructural investigations indicated that the Ba0.5Sr0.5TiO3 (BST) had grown epitaxially onto the SrRuO3 lower electrode, inducing in-plane compressive and out- of-plane tensile strain in the BST. The magnitude of strain developed increased systematically as film thickness decreased. At room temperature this composition of BST is paraelectric in bulk. However, polarization measurements suggested that strain had stabilized the ferroelectric state, and that the decrease in film thickness caused an increase in remanent polarization. An increase in the paraelectric-ferroelectric transition temperature upon a decrease in thickness was confirmed by dielectric measurements. Polarization loops were fitted to Landau-Ginzburg-Devonshire (LGD) polynomial expansion, from which a second order paraelectric-ferroelectric transition in the films was suggested at a thickness of similar to500 nm. Further, the LGD analysis showed that the observed changes in room temperature polarization were entirely consistent with strain coupling in the system. (C) 2002 American Institute of Physics.

An isothermal-isobaric Langevin thermostat for simulating nanoparticles under pressure: Application to Au clusters

We present a method for simulating clusters or, molecules subjected to an external pressure, which is exerted by a pressure-transmitting medium. It is based on the canoninical Langevin thermostat, but extended in such a way that the Brownian forces are allowed to operate only from the region exterior to the cluster. We show that the frictional force of the Langevin thermostat is linked to the pressure of the reservoir in a unique way, and that this property manifests itself when the particle it acts upon is not pointlike but has finite dimensions. By choosing appropriately the strength of the random forces and the friction coefficient, both temperature and pressure can be controlled independently. We illustrate the capabilities of this new method by calculating the compressibility of small gold clusters under pressure.

The practical implications of using standardized estimation equations in calculating the prevalence of chronic kidney disease

Background. Kidney Disease Outcomes Quality Initiative (KDOQI) chronic kidney disease (CKD) guidelines have focused on the utility of using the modified four-variable MDRD equation (now traceable by isotope dilution mass spectrometry IDMS) in calculating estimated glomerular filtration rates (eGFRs). This study assesses the practical implications of eGFR correction equations on the range of creatinine assays currently used in the UK and further investigates the effect of these equations on the calculated prevalence of CKD in one UK region Methods. Using simulation, a range of creatinine data (30–300 µmol/l) was generated for male and female patients aged 20–100 years. The maximum differences between the IDMS and MDRD equations for all 14 UK laboratory techniques for serum creatinine measurement were explored with an average of individual eGFRs calculated according to MDRD and IDMS 30 ml/min/1.73 m2. Observed data for 93,870 patients yielded a first MDRD eGFR 3 months later of which 47 093 (71%) continued to have an eGFR

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Resting energy expenditure in non-ventilated, non-sedated patients recovering from serious traumatic brain injury: Comparison of prediction equations with indirect calorimetry values

Background & aims: Little is known about energy requirements in brain injured (TBI) patients, despite evidence suggesting adequate nutritional support can improve clinical outcomes. The study aim was to compare predicted energy requirements with measured resting energy expenditure (REE) values, in patients recovering from TBI.

Methods: Indirect calorimetry (IC) was used to measure REE in 45 patients with TBI. Predicted energy requirements were determined using FAO/WHO/UNU and Harris–Benedict (HB) equations. Bland– Altman and regression analysis were used for analysis.

Results: One-hundred and sixty-seven successful measurements were recorded in patients with TBI. At an individual level, both equations predicted REE poorly. The mean of the differences of standardised areas of measured REE and FAO/WHO/UNU was near zero (9 kcal) but the variation in both directions was substantial (range 591 to þ573 kcal). Similarly, the differences of areas of measured REE and HB demonstrated a mean of 1.9 kcal and range 568 to þ571 kcal. Glasgow coma score, patient status, weight and body temperature were signi?cant predictors of measured REE (p < 0.001; R²⁼ 0.47).

Conclusions: Clinical equations are poor predictors of measured REE in patients with TBI. The variability in REE is substantial. Clinicians should be aware of the limitations of prediction equations when estimating energy requirements in TBI patients.