Additional Linear Term Research Articles

Two-temperature thermochemical nonequilibrium model based on the coarse-grained treatment of molecular vibrational states.

Although the high-fidelity state-to-state (StS) model accurately describes high-temperature thermochemical nonequilibrium flows, its practical application is hindered by the prohibitively high computational cost. In this paper, we develop a reduced-order model that leverages the widelyused two-temperature (2T) framework and a coarse-grained treatment of molecular vibrational states to achieve accuracy comparable to the StS model while ensuring computational efficiency. We observe that the multigroup coarse-grained model (CGM), lumping vibrational energy levels into several groups, yields results close to the StS model for the high-temperature postshock oxygen flows, even using only two groups. However, theone-group CGM (CGM-1G), equivalent to the 2T model but using the StS kinetics, fails to approximate the StS results. Analysis of microscopic group properties reveals that the failure of the CGM-1G stems from the inability to capture the non-Boltzmann effects of mid-to-high vibrational levels, overestimating apparent dissociation rates and vibrational energy loss in the dissociation-dominated region. We then propose an analytical distribution function of vibrational groups by incorporating Treanor-like terms and an additional linear term (addressing the dissociation depletion of high-lying levels). Building upon this algebraic group distribution function and reconstructing vibrational levels within each group using the vibrational temperature, we develop a new 2T model called CG2T, which demonstrates accuracy much closer (than the CGM-1G) to the StS results for the postshock oxygen flows with varying degrees of thermochemical nonequilibrium. Moreover, a fullyconnected neural network is pretrained to substitute the module for the mass and vibrational energy source terms to enhance computational efficiency, achieving about 30-fold speedup in the CG2T model without sacrificing accuracy.

Searching for Unconventional Superfluid in Excitons of Monolayer Semiconductors.

It is well known that two-dimensional (2D) bosons in homogeneous space cannot undergo real Bose-Einstein condensation, and the superfluid to normal phase transition is Berezinskii-Kosterlitz-Thouless (BKT) type, associated with vortex-antivortex pair unbinding. Here we point out a 2D bosonic system whose low energy physics goes beyond conventional paradigm of 2D homogeneous bosons, i.e., intralayer excitons in monolayer transition metal dichalcogenides. With intrinsic valley-orbit coupling and valley Zeeman energy, exciton dispersion becomes linear at small momentum, giving rise to a series of novel features. The critical temperature of Bose-Einstein condensation of these excitons is nonzero, suggesting true long-range order in 2D homogeneous system. The dispersion of Goldstone mode at long wavelength has the form ϵ(q)∼sqrt[q], in contrast to conventional linear phonon spectrum. The vortex energy deviates from the usual logarithmic form with respect to system size, but instead has an additional linear term. Superfluid to normal phase transition is no longer BKT type for system size beyond a characteristic scale, without discontinuous jump in superfluid density. With the recent experimental progress on exciton fluid at thermal equilibrium in monolayer semiconductors, our work points out an experimentally accessible system to search for unconventional 2D superfluids beyond BKT paradigm.

Analysis of a reactive porous separation effects on depollution and indoor air quality: Application of LBM-MRT to heat and mass transfers

The reduction of energy demand and the indoor air quality associated with energy demand are the main goals of thermal buildings. This work is devoted to the study of the effect of a reactive porous separation on the ventilation (cooling) and depollution capacity in a rectangular room ventilated by air displacement. The model is considered as a cavity heated on its right verticle wall and thermally isolated by the other three walls. A porous separation divides the room into two compartments. The system of equations was solved using the Lattice Boltzmann method with multiple relaxation times. The extended Darcy Brinkman-Forchheimer model was used to simulate the porous material. An additional linear term is added to the standard transport equations (material diffusion) to account for reaction effects, this term was derived from Arrhenius' law. Over a wide range of Richardson and Darcy numbers, the results of the computations show the influence of these parameters on the flow structure, making it possible to categorize the different convection phenomena (natural, forced and mixed). The most important point to note is that the addition of reaction (fixing reaction) improves indoor air quality and can achieve a 55 % reduction in air renewal time, thus saving on energy costs. However, this reactif effect has no influence on the thermal efficiency of the proposed model.

Multiple scattering theory for modeling sonic booms in atmospheric turbulence.

Sonic booms are often modeled using Burgers equations accounting for dominant propagation effects. Scattering effects of turbulence, however, have not been incorporated into such equations, although these effects are ubiquitous in measured sonic booms. This paper formulates the mean scattering effects, including backscattering, using multiple scattering theory and ensemble averaging. It obtains an acousto-turbulence interaction energy representing the interaction of an acoustic wavefield with a turbulence field. The interaction energy gives rise to a scattering wavenumber, a complex-valued correction to the free-space wavenumber. The scattering wavenumber leads to a dispersion and attenuation of the mean waveform due to backscattering, and can be obtained from a derived exact solution. An existing Burgers equation is extended to include the scattering effects of turbulence as an additional linear term. Numerical simulations of an N-wave and a low boom show that the mean scattering effects lead to shock thickening in the mean waveforms as well as reduce the peak amplitudes and total energy contents. The energy reduction is less severe in the low boom than in the N-wave and is dependent on the variance, correlation length, and thickness of the turbulence field.

Characterization of the Bakelite Prototype Sensor for NEWS-G

The New Experiments With Spheres - Gas (NEWS-G) group at Queen's University uses Spherical Proportional Counters (SPCs) in the search for dark matter. Incoming radiation interacts with the gas inside the SPC through ionization, producing electron/ion pairs [1]. These primary electrons drift towards the central anode under the influence of an electric field [1]. A secondary ionization, termed avalanche, occurs at distances proportional to the size of the anode resulting in the multiplication of charges [1]. The signal that is produced is proportional to the number of secondary charges created during the avalanche [1]. A 30 cm-diameter sphere was used to characterize a six anode, spherical Bakelite prototype sensor. The sensor is divided into north and south three-anode read-out channels. To study the detector's response, an Fe55 source was placed inside the sphere, which was then filled with 1 bar of 40Ar+CH4 2% gas. The source was moved around the sphere with thirty-second data-taking runs taken at each point and high voltages applied to each channel. Cuts were applied to the event properties to isolate the 5.9 keV Fe55 peak. The peak was plotted as a histogram and fit with a Gaussian function with two additional linear terms. The gain and resolution of the sensor were extracted from the fit parameters. The channel dominance change angle was calculated by interpolating the number of events recorded by each channel at each point on the sphere. The gain, number of events and the channel dominance change angle were mapped on the sphere between 20 and 40 cm arc length in the theta direction, and all the way around the sphere in the phi direction to improve the understanding of the Bakelite sensor.

Nonlinear vibrations of a composite circular plate with a rigid body

The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton’s principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.

Online Apprenticeship Learning

In Apprenticeship Learning (AL), we are given a Markov Decision Process (MDP) without access to the cost function. Instead, we observe trajectories sampled by an expert that acts according to some policy. The goal is to find a policy that matches the expert's performance on some predefined set of cost functions. We introduce an online variant of AL (Online Apprenticeship Learning; OAL), where the agent is expected to perform comparably to the expert while interacting with the environment. We show that the OAL problem can be effectively solved by combining two mirror descent based no-regret algorithms: one for policy optimization and another for learning the worst case cost. By employing optimistic exploration, we derive a convergent algorithm with O(sqrt(K)) regret, where K is the number of interactions with the MDP, and an additional linear error term that depends on the amount of expert trajectories available. Importantly, our algorithm avoids the need to solve an MDP at each iteration, making it more practical compared to prior AL methods. Finally, we implement a deep variant of our algorithm which shares some similarities to GAIL, but where the discriminator is replaced with the costs learned by OAL. Our simulations suggest that OAL performs well in high dimensional control problems.

Validation of a sonic boom model through atmospheric turbulence with flight test data

This paper presents a validation of an extended Burgers equation that accounts for mean scattering effects of turbulence in the atmospheric boundary layer (ABL). The scattering effects are calculated from a scattering wavenumber formulated using the multiple scattering theory and are incorporated as an additional linear term in a Burgers equation commonly used to model sonic boom propagation. The scattering wavenumber represents the interaction of an acoustic wavefield, including backscattering, with a turbulent field and gives rise to signal attenuation and distortion. Numerical models obtained using the extended Burgers equation are compared to measured sonic booms from conventional supersonic aircraft. The acoustic measurements are supplemented by measurements of the turbulence conditions as well as the thickness of the ABL. Results show that the mean effects of scattering on sonic booms smooth out shocks in the waveforms, reduce the peak amplitudes, and thus reduce the loudness. The results also indicate that the loudness reduction is dependent on the variance, correlation length, and thickness of the turbulent field. The performance of the extended Burgers equation is compared to that of existing signal processing-based approaches developed to represent turbulence effects on sonic booms through the ABL.

О симметриях обобщенного уравнения Кортевега–де Фриза

The Korteweg–de Vries equation is a third–order nonlinear partial differential equation that plays an important role in the theory of nonlinear waves, mainly of hydrodynamic origin. It was first obtained by Joseph Boussinesq in 1877, but a detailed analysis was already carried out by Diederik Korteweg and Gustav de Vries in 1895. The Korteweg–de Vries equation, its analogues and generalizations arise in mathematical models in a variety of subject areas. There are at least several thousand publications in which the Korteweg–de Vries equation is considered from one side or another, and the authors are aware of the impossibility of writing at least a simple list listing these publications. Nevertheless, it is possible to mention, for example, The paper considers some generalization of the Korteweg–de Vries equation obtained by introducing an arbitrary function with respect to which a group classification is performed. The admissible operators of the generalized Korteweg–de Vries equation, the basic algebra of admissible operators and possible cases of extension of the algebra of admissible operators for a coefficient function of a special kind are found. Tables of commutators of the obtained algebras are also calculated. At the same time, the fact of isomorphism of admissible algebras in two different cases of specification of the function-coefficient of the generalized Korteweg–de Vries equation is noted. It is shown that the maximum possible dimension of the algebra of admissible operators is equal to four and corresponds to the almost classical Korteweg–de Vries equation with a possible additional linear term. In all other cases, if the resulting algebra of admissible operators and extends, then to a three-dimensional Lie algebra.

The complex Monge–Ampère equation with a gradient term

We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

Exact and approximated solutions for the harmonic and anharmonic repulsive oscillators: Matrix method

We study the repulsive harmonic oscillator and an extension of this system, with an additional linear anharmonicity term. The system is solved in exact and perturbative form, the latter by using the so-called normalized perturbative matrix method. The perturbative solution up to second order is compared with the exact solution when the system is initially in coherent and a Schrodinger-cat states.

Polydispersity and surface energy strength in nematic colloids

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an free energy functional with an additional linear term, which may be interpreted as an effective field induced by the inclusions. Moreover, we compute the free energy in a regime of very strong anchoring, that is, when the surface energy effects dominate over the volume free energy.

Tracking Performance of Robust RLS Algorithm for MIMO Channel Estimation

A robust recursive least square (RRLS) algorithm that has been designed for SISO communications by Bhotto and Antoniou (IEEE Signal Process Lett 18(3):185–188, 2011) is unable to work for MIMO system because of single error constraint. In this paper, a modified version of RRLS algorithm with the application of MIMO channel estimation is introduced. An RRLS algorithm is modified in such a way that it can provide much faster convergence rate in MIMO channel estimation than that of RLS and variable forgetting factor RLS (VFF-RLS) algorithms. Moreover, the optimum forgetting factor is derived for MIMO RRLS in order to minimize the error function. Simulation results show that the MIMO RRLS provides fast convergence performance as compared to RLS and VFF-RLS algorithms without additional multiplication complexity, however, an additional linear term of N in the addition complexity of modified MIMO RRLS does not enhance its computational complexity and keeps it almost equivalent to those of RLS and VFF-RLS algorithms. Moreover, it is observed that the optimum forgetting factor is highly dependent on RRLS scaling parameter, $$E_b/N_o$$, doppler shift and number of antennas.

Phenomenological model of aluminium-hole ([AlO4/h+]0) defect formation in sedimentary quartz upon room temperature irradiation: electron spin resonance (ESR) study

The mechanism governing the production of the paramagnetic [AlO4/h+]0 centres (denoted also as Al-hole or Al-h) in quartz as a function of given dose is of great importance in electron spin resonance (ESR) dating, as the analytical function used to characterise the evolution of this centre with accumulated dose is used to derive the equivalent dose by extrapolation to the abscissa-axis. The single saturating exponential model fails to accurately represent the dose response curve especially at high doses, and consequently, empirical functions, such as a saturating exponential plus a linear term, are widely used in the dating community. Herein, a physical phenomenological model is presented to describe the Al-hole formation under gamma irradiation in sedimentary quartz. Based on previous studies it is known that the Al-hole centre is formed via the dissociation of the Al centres compensated with alkali ions [AlO4/M+]0 (generally denoted as Al-M) where M+ could be Li+, Na+ or K+, as well as by the dissociation of Al compensated with hydrogen ions [AlO4/H+]0, (denoted as Al–H). When irradiation moves interstitial alkali ions away from the aluminium ions, they can be replaced by H+ ions beside the conversion to Al-hole centres. By assuming that the rate of the dissociation process is proportional to the concentration of the defects themselves, a sum of saturating exponential functions is obtained for describing the growth of Al-hole with dose. The model is applied on data obtained on sedimentary quartz specimens of different origins for describing the dose response of the paramagnetic Al-hole ESR signal. We are showing that the signal of Al-hole does not reach full saturation at doses even as high as 100 kGy and can it be well represented by two exponential components as predicted by the model. As such, the additional linear term reported by other works when describing the dose response is just a first order approximation of one of the saturating exponential functions.

Free vibration analysis of a spinning piezoelectric beam with geometric nonlinearities

The linear and non-linear free vibrations of a spinning piezoelectric beam are studied by considering geometric nonlinearities and electromechanical coupling effect. The non-linear differential equations of the spinning piezoelectric beam governing two transverse vibrations are derived by using transformation of two Euler angles and the extended Hamilton principle, wherein an additional piezoelectric coupling term and different linear terms are present in contrast to the traditional shaft model. Linear frequencies are obtained by solving the standard eigenvalues of the linearized system directly, and the non-linear frequencies and non-linear complex modes are achieved by using the method of multiple scales. For free vibrations analysis of a spinning piezoelectric beam, the non-linear modal motions are investigated as forward and backward precession with different spinning speeds. The responses to the initial conditions for this gyroscopic system are studied and a beat phenomenon is found, which are then validated by numerical simulation. The influences of some parameters such as electrical resistance, rotary inertia and spinning speeds to the non-linear dynamics of a spinning piezoelectric beam are investigated.

Dynamic properties of micro-magnetic noise in soft ferromagnetic materials

Dynamic response of magnetic hysteresis, magnetic Barkhausen noise and magneto-acoustic emission in a soft ribbon and electrical steels was studied comprehensively. The measurements were performed under controllable magnetization conditions: sinusoidal/triangular waveforms of the magnetic induction and a triangular waveform of the magnetic field. Magnetizing frequency was varied in a wide range: fmag=0.5–500 and 0.5–100 Hz for the ribbon and the electrical steels, respectively. Magnetization amplitude was fixed on a near-saturation level Hmax≃100 A/m. Barkhausen noise signal was detected by a sample-wrapping/surface-mounted coil and differently filtered. It was found that intensity of the Barkhausen noise rises approximately as a square root function of the magnetizing frequency. Whereas, level of the magneto-acoustic emission follows the hysteresis loss trend with an additional linear term (classical loss component).

Cascade replication of dissipative solitons.

We report a new effect of a cascade replication of dissipative solitons from a single one. It is discussed in the framework of a common model based on the one-dimensional cubic-quintic complex Ginzburg-Landau equation in which an additional linear term is introduced to account the perturbation from a particular potential of externally applied force. The effect is demonstrated on the light beams propagating through a planar waveguide. The waveguide consists of a nonlinear layer able to guide dissipative solitons and a magneto-optic substrate. In the waveguide an externally applied force is considered to be an inhomogeneous magnetic field which is induced by modulated electric currents flowing along a set of conducting wires adjusted on the top of the waveguide.

Blazed diffraction gratings produced by ion bombardment of pre-patterned solid surfaces

We propose a method of producing high quality blazed gratings and carry out simulations of it. By combining the near perfect periodicity produced by conventional lithographic methods with the tendency of ion sputtering to produce terraced topographies, this fabrication procedure could produce highly ordered, faceted surfaces on amorphous materials. Our approach differs from previous uses of ion bombardment to fabricate blazed gratings, and has the unique advantage that it could be used as the initial step in the fabrication of high efficiency multilayer-coated blazed gratings. Our numerical investigations of the relevant equations of motion demonstrate that our method produces efficient blazed gratings for a broad range of parameter values. We also develop concrete predictions regarding the optimal implementation of our proposed procedure, and show that high quality blazed gratings can emerge even if additional linear or nonlinear terms are present in the equation of motion.

Control of dissipative solitons in a magneto-optic planar waveguide.

We propose a mechanism to control propagation of a group of stable dissipative solitons in a nonlinear magneto-optic planar waveguide. The control is realized by means of a spatially inhomogeneous external magnetic field, which is induced by a set of direct conducting wires placed on the top of the guiding layer. The wires are extended in the direction of soliton propagation, and carry electric currents with particular piecewise constant profiles. In order to describe the soliton evolution the one-dimensional cubic-quintic complex Ginzburg-Landau equation has been adapted by tailoring an additional linear term, which is responsible for the magneto-optic effect.

KPZ Reloaded

We analyze the one-dimensional periodic Kardar-Parisi-Zhang equation in the language of paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer. Apart from deriving a basic existence and uniqueness result for paracontrolled solutions to the KPZ equation we perform a thorough study of some related problems. We rigorously prove the links between KPZ equation, stochastic Burgers equation, and (linear) stochastic heat equation and also the existence of solutions starting from quite irregular initial conditions. We also build a partial link between energy solutions as introduced by Goncalves and Jara and paracontrolled solutions. Interpreting the KPZ equation as the value function of an optimal control problem, we give a pathwise proof for the global existence of solutions and thus for the strict positivity of solutions to the stochastic heat equation. Moreover, we study Sasamoto-Spohn type discretizations of the stochastic Burgers equation and show that their limit solves the continuous Burgers equation possibly with an additional linear transport term. As an application, we give a proof of the invariance of the white noise for the stochastic Burgers equation which does not rely on the Cole-Hopf transform.