Academic literature on the topic 'Single parameter scaling theory'

Abstract In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter $\unicode[STIX]{x1D701}\geqslant 0$, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets ($\unicode[STIX]{x1D701}<10^{-3}$) hardly pierce the bubble, but remain within it throughout the collapse and rebound. Intermediate jets ($10^{-3}<\unicode[STIX]{x1D701}<0.1$) pierce the opposite bubble wall close to the last collapse phase and clearly emerge during the rebound. Strong jets ($\unicode[STIX]{x1D701}>0.1$) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of $\unicode[STIX]{x1D701}$, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets ($\unicode[STIX]{x1D701}<0.1$) depend only on $\unicode[STIX]{x1D701}$, not on the jet driver (i.e. gravity or boundaries). In the same regime, the jet parameters are found to be well approximated by power laws of $\unicode[STIX]{x1D701}$, which we explain through analytical arguments.

The dependences of the longitudinal and Hall resistances on a magnetic field in n-InGaAs/GaAs heterostructures with a single and double quantum wells after infrared illumination are measured in the range of magnetic fields B=0-16 T and temperatures T=0.05-4.2 K. Analysis of the experimental results was carried out on a base of two-parameter scaling hypothesis for the integer quantum Hall effect. The value of the second (irrelevant) critical exponent of the theory of two-parameter scaling was estimated. DOI: 10.21883/FTP.2017.02.44119.8302

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.

AbstractThis study offers a unified formulation of single- and multimoment normalizations of the raindrop size distribution (DSD), which have been proposed in the framework of scaling analyses in the literature. The key point is to consider a well-defined “general distribution” g(x) as the probability density function (pdf) of the raindrop diameter scaled by a characteristic diameter Dc. The two-parameter gamma pdf is used to model the g(x) function. This theory is illustrated with a 3-yr DSD time series collected in the Cévennes region, France. It is shown that three DSD moments (M2, M3, and M4) make it possible to satisfactorily model the DSDs, both for individual spectra and for time series of spectra. The formulation is then extended to the one- and two-moment normalization by introducing single and dual power-law models. As compared with previous scaling formulations, this approach explicitly accounts for the prefactors of the power-law models to yield a unique and dimensionless g(x), whatever the scaling moment(s) considered. A parameter estimation procedure, based on the analysis of power-law regressions and the self-consistency relationships, is proposed for those normalizations. The implementation of this method with different scaling DSD moments (rain rate and/or radar reflectivity) yields g(x) functions similar to the one obtained with the three-moment normalization. For a particular rain event, highly consistent g(x) functions can be obtained during homogeneous rain phases, whatever the scaling moments used. However, the g(x) functions may present contrasting shapes from one phase to another. This supports the idea that the g(x) function is process dependent and not “unique” as hypothesized in the scaling theory.

As an application of perfect lattice perturbation theory, we construct an O(λ) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space, we obtain a set of 2-spin and 4-spin couplings ∝λ, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(λ) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps ΔE1, ΔE2 and for the scaling quantity ΔE2/ΔE1 in different regimes of the interaction parameter, and of the correlation length. For the quartic oscillator — which corresponds to an asymptotically free theory — we also discuss a classically perfect action. The single gaps perform very well, which corresponds to a clearly improved asymptotic scaling. On the other hand, it turns out to be difficult to demonstrate an improvement for the scaling ratio.

Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton’s component vortices. The dynamics display a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons, which are parallel to the vertical axis and have zero horizontal separation, do not move and do not transport fluid. Horizontally aligned hetons, which lie on the horizontal plane and have zero vertical separation, have a single parameter, the horizontal vortex half-separation Y, and simple scaling shows the dimensional trapped volume scales as Y3. Tilted hetons are described by two parameters, Y and the vertical vortex half-separation Z, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as Z4/Y for large Z. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory.

The surface of superground Mn-Zn ferrite single crystal may be identified as a self-affine fractal in the stochastic sense. The rms roughness increased as a power of the scale from 102 nm to 106 nm with the roughness exponent α=0.17±0.04, and 0.11±0.06, for grinding feed rate of 15 and 10 μm/rev, respectively. The scaling behavior coincided with the theory prediction well used for growing self-affine surfaces in the interested region for magnetic heads performance. The rms roughnesses increased with increase in the feed rate, implying that the feed rate is a crucial grinding parameter affecting the supersmooth surface roughness in the machining process.

Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp−bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1−φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3−φ and S~A2−φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni50Mn28.5Ga21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1−φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.

A polymer is a large molecule constructed from many smaller structural units called<br/>monomers joined together by covalent bonds. Polymers have existed in natural form<br/>since life began and those such as DNA, RNA, proteins and polysaccharides are some<br/>of the most important macromolecules found in plant and animal life. From the earliest<br/>times, the man has used many of these polymers as materials for providing clothing,<br/>decoration, tools, weapons and other requirements. However, the origins of today's<br/>polymer industry commonly are accepted as being in the nineteenth century when<br/>important discoveries were made concerning to the modification of certain natural<br/>polymers, as cellulose. The use of synthetic and natural polymers as stabilisers for<br/>colloid systems (sols, dispersions, microemulsions, etc.) is becoming more important<br/>everyday in contemporary life. Polymer additives can be applied in preconcentrations<br/>and dehydration of suspensions in mineral processing, purification of wastewater and<br/>even in nutritional and pharmaceutical emulsions being their importance related to the<br/>characteristics of the process and the properties that they show. The present work aims<br/>to develop appropriate numerical and analytical modelling techniques, which can<br/>describe (considering the formation of loops and tails) the structure of a polymeric layer<br/>adsorbed on heterogeneous surfaces; this adsorbed layer is an relevant factor in the<br/>properties showed by this kind of materials. Taking into account this, the methodology<br/>known as Single Chain Mean Field (SCMF) (originally used to study micellar<br/>aggregates and grafted polymers) was modified to apply on polymer adsorption<br/>problems. In this way, it was possible to calculate numerically properties that can be<br/>experimentally measured, such as total monomer volume fraction profiles, loop and tail<br/>volume fraction profiles, adsorbance or the thickness of the adsorbed layer. The<br/>structure of the polymeric layer was examined both for flat and spherical (colloidal<br/>particles) surface geometries. When compared with other well established<br/>methodologies for the numerical simulation of polymeric systems, this new version of<br/>SCMF was found to be more efficient due to the improved sampling of the polymer<br/>chain configuration space.<br/>Thus, SCMF method results, in the case of the adsorption on flat surfaces, compare well<br/>with those obtained either with Monte Carlo simulations or with the method developed<br/>in the 80s by Scheutjens and Fleer (SCF). Due to the lack of studies focusing to polymer<br/>adsorption on colloidal particles, our results have been the first to present quantitative<br/>predictions of the structure of the polymeric layer adsorbed on a spherical surface. Thus,<br/>we have demonstrated the dependence of the adsorbed polymer layer with the size of<br/>the colloidal particle as well as the characteristic lengths that influence on it. Finally, in<br/>this work an analytical approach for the description of polymer-colloidal mixtures has<br/>been developed which compares well with the numerical results obtained from the<br/>SCMF methodology. Furthermore, the analytical approach is able to predict system<br/>behaviours, as for example the formation of gels.<br>Un polímero es una molécula de grandes dimensiones formada de pequeñas unidades<br/>llamadas monómeros, los cuales se encuentran unidos por medio de enlaces covalentes.<br/>Los polímeros han existido de forma natural desde el comienzo de la vida, y aquellos<br/>como el DNA, RNA o las proteínas son algunos de los polímeros más importantes<br/>encontrados tanto en la vida animal como en la vegetal. Desde siempre el hombre ha<br/>utilizado muchos de estos polímeros como materiales para hacer ropa, decoración,<br/>herramientas, etc. Sin embargo, el origen de la industria de polímeros que conocemos<br/>hoy en día se produjo en el siglo 19, gracias a importantes descubrimientos dentro de la<br/>modificación de ciertos polímeros naturales, como la celulosa. El uso de polímeros<br/>sintéticos y naturales como estabilizadores de sistemas coloidales (dispersiones,<br/>microemulsiones, etc.) juega en nuestros días un papel importante. Los polímeros<br/>utilizados como aditivos, pueden ser aplicados en preconcentraciones y deshidratación<br/>de suspensiones dentro de procesos minerales, tratamiento de aguas residuales e incluso<br/>los podemos encontrar dentro de la industria farmacéutica y alimentaria, donde su<br/>importancia es debida a la procesabilidad y propiedades que ellos exhiben. El trabajo<br/>que se presenta es orientado al desarrollo de técnicas de modelización, tanto analíticas<br/>como computacionales, y su aplicación en la descripción (por medio de la formación de<br/>bucles y colas) de la estructura de la capa de polímeros adsorbida en superficies<br/>heterogéneas, siendo dicha capa de polímeros un factor importante en las propiedades<br/>que este tipo de materiales presentan. Con este propósito, la metodología conocida<br/>como Single Chain Mean Field, utilizada anteriormente tanto para el estudio de<br/>agregados micelares como de polímeros anclados en superficies, ha sido modificada<br/>para describir la adsorción de polímeros en superficies. Así se han podido calcular<br/>numéricamente propiedades medibles experimentalmente como los perfiles de la<br/>fracción en volumen de monómeros totales, además de los pertenecientes a los bucles y<br/>colas, adsorbancia o el espesor de la capa adsorbida, para geometrías de la superficie<br/>absorbente tanto plana como esférica (partículas coloidales). En su comparación con<br/>otras metodologías, ya establecidas para la simulación numérica dentro de la física de<br/>polímeros, la aplicación de esta nueva versión del Single Chain Mean Field (SCMF)<br/>ha resultado ser más eficiente debido a un mejor muestreo del espacio de<br/>configuraciones de las cadenas poliméricas. De este modo, comparando los resultados<br/>obtenidos a partir del SCMF, con aquellos obtenidos mediante técnicas de simulación<br/>Monte Carlo o la teoría desarrollada en los años 80 por Scheutjens y Fleer (SCF), se ha<br/>podido encontrar un buen acuerdo en las propiedades calculadas para el caso de la<br/>adsorción en superficies planas. Debido a la dificultad intrínseca del estudio de la<br/>adsorción en superficies curvadas, nuestros resultados son los primeros que presentan<br/>predicciones cuantitativas sobre la estructura de la capa que se forma sobre una<br/>partícula coloidal. Así hemos podido comprobar la dependencia de la estructura de la<br/>capa de polímeros adsorbidos con el tamaño de la partícula sobre la que se encuentran<br/>adsorbidos además de las longitudes características de las cuales depende. Finalmente,<br/>en este trabajo se ha desarrollado, también, una teoría analítica para la descripción de la<br/>mezcla polímero-coloide. De este modo, los resultados numéricos obtenidos con el<br/>SCMF han podido ser comparados con dicha teoría, obteniendo, de nuevo, un buen<br/>acuerdo y predecir, además, comportamientos colectivos como la formación de geles.

Durante la última década y paralelamente al incremento de la velocidad de computación, las técnicas de simulación molecular se han erigido como una importante herramienta para la predicción de propiedades físicas de sistemas de interés industrial. Estas propiedades resultan esenciales en las industrias química y petroquímica a la hora de diseñar, optimizar, simular o controlar procesos. El actual coste moderado de computadoras potentes hace que la simulación molecular se convierta en una excelente opción para proporcionar predicciones de dichas propiedades. En particular, la capacidad predictiva de estas técnicas resulta muy importante cuando en los sistemas de interés toman parte compuestos tóxicos o condiciones extremas de temperatura o presión debido a la dificultad que entraña la experimentación a dichas condiciones. La simulación molecular proporciona una alternativa a los modelos termofísicos utilizados habitualmente en la industria como es el caso de las ecuaciones de estado, modelos de coeficientes de actividad o teorías de estados correspondientes, que resultan inadecuados al intentar reproducir propiedades complejas de fluidos como es el caso de las de fluidos que presentan enlaces de hidrógeno, polímeros, etc. En particular, los métodos de Monte Carlo (MC) constituyen, junto a la dinámica molecular, una de las técnicas de simulación molecular más adecuadas para el cálculo de propiedades termofísicas. Aunque, por contra del caso de la dinámica molecular, los métodos de Monte Carlo no proporcionan información acerca del proceso molecular o las trayectorias moleculares, éstos se centran en el estudio de propiedades de equilibrio y constituyen una herramienta, en general, más eficiente para el cálculo del equilibrio de fases o la consideración de sistemas que presenten elevados tiempos de relajación debido a su bajos coeficientes de difusión y altas viscosidades. Los objetivos de esta tesis se centran en el desarrollo y la mejora tanto de algoritmos de simulación como de potenciales intermoleculares, factor considerado clave para el desarrollo de las técnicas de simulación de Monte Carlo. En particular, en cuanto a los algoritmos de simulación, la localización de puntos críticos de una manera precisa ha constituido un problema para los métodos habitualmente utilizados en el cálculo de equlibrio de fases, como es el método del colectivo de GIBBS. La aparición de fuertes fluctuaciones de densidad en la región crítica hace imposible obtener datos de simulación en dicha región, debido al hecho de que las simulaciones son llevadas a cabo en una caja de simulación de longitud finita que es superada por la longitud de correlación. Con el fin de proporcionar una ruta adecuada para la localización de puntos críticos tanto de componentes puros como mezclas binarias, la primera parte de esta tesis está dedicada al desarrollo y aplicación de métodos adecuados que permitan superar las dificultades encontradas en el caso de los métodos convencionales. Con este fin se combinan estudios de escalado del tamaño de sitema con técnicas de "Histogram Reweighting" (HR). La aplicación de estos métodos se ha mostrado recientemente como mucho mejor fundamentada y precisa para el cálculo de puntos críticos de sistemas sencillos como es el caso del fluido de LennardJones (LJ). En esta tesis, estas técnicas han sido combinadas con el objetivo de extender su aplicación a mezclas reales de interés industrial. Previamente a su aplicación a dichas mezclas reales, el fluido de LennardJones, capaz de reproducir el comportamiento de fluidos sencillos como es el caso de argón o metano, ha sido tomado como referencia en un paso preliminar. A partir de simulaciones realizadas en el colectivo gran canónico y recombinadas mediante la mencionada técnica de "Histogram Reweighting" se han obtenido los diagramas de fases tanto de fluidos puros como de mezclas binarias. A su vez se han localizado con una gran precisión los puntos críticos de dichos sistemas mediante las técnicas de escalado del tamaño de sistema. Con el fin de extender la aplicación de dichas técnicas a sistemas multicomponente, se han introducido modificaciones a los métodos de HR evitando la construcción de histogramas y el consecuente uso de recursos de memoria. Además, se ha introducido una metodología alternativa, conocida como el cálculo del cumulante de cuarto orden o parámetro de Binder, con el fin de hacer más directa la localización del punto crítico. En particular, se proponen dos posibilidades, en primer lugar la intersección del parámetro de Binder para dos tamaños de sistema diferentes, o la intersección del parámetro de Binder con el valor conocido de la correspondiente clase de universalidad combinado con estudios de escalado. Por otro lado, y en un segundo frente, la segunda parte de esta tesis está dedicada al desarrollo de potenciales intermoleculares capaces de describir las energías inter e intramoleculares de las moléculas involucradas en las simulaciones. En la última década se han desarrolldo diferentes modelos de potenciales para una gran variedad de compuestos. Uno de los más comunmente utilizados para representar hidrocarburos y otras moléculas flexibles es el de átomos unidos, donde cada grupo químico es representado por un potencial del tipo de LennardJones. El uso de este tipo de potencial resulta en una significativa disminución del tiempo de cálculo cuando se compara con modelos que consideran la presencia explícita de la totalidad de los átomos. En particular, el trabajo realizado en esta tesis se centra en el desarrollo de potenciales de átomos unidos anisotrópicos (AUA), que se caracterizan por la inclusión de un desplazamiento de los centros de LennardJones en dirección a los hidrógenos de cada grupo, de manera que esta distancia se convierte en un tercer parámetro ajustable junto a los dos del potencial de LennardJones.<br/>En la segunda parte de esta tesis se han desarrollado potenciales del tipo AUA4 para diferentes familias de compuesto que resultan de interés industrial como son los tiofenos, alcanoles y éteres. En el caso de los tiofenos este interés es debido a las cada vez más exigentes restricciones medioambientales que obligan a eliminar los compuestos con presencia de azufre. De aquí la creciente de necesidad de propiedades termodinámicas para esta familia de compuestos para la cual solo existe una cantidad de datos termodinámicos experimentales limitada. Con el fin de hacer posible la obtención de dichos datos a través de la simulación molecular hemos extendido el potencial intermolecular AUA4 a esta familia de compuestos. En segundo lugar, el uso de los compuestos oxigenados en el campo de los biocombustibles ha despertado un importante interés en la industria petroquímica por estos compuestos. En particular, los alcoholes más utilizados en la elaboración de los biocombustibles son el metanol y el etanol. Como en el caso de los tiofenos, hemos extendido el potencial AUA4 a esta familia de compuestos mediante la parametrización del grupo hidroxil y la inclusión de un grupo de cargas electrostáticas optimizadas de manera que reproduzcan de la mejor manera posible el potencial electrostático creado por una molecula de referencia en el vacío. Finalmente, y de manera análoga al caso de los alcanoles, el último capítulo de esta tesis la atención se centra en el desarrollo de un potencial AUA4 capaz de reproducir cuantitativamente las propiedades de coexistencia de la familia de los éteres, compuestos que son ampliamente utilizados como solventes.<br>Parallel with the increase of computer speed, in the last decade, molecular simulation techniques have emerged as important tools to predict physical properties of systems of industrial interest. These properties are essential in the chemical and petrochemical industries in order to perform process design, optimization, simulation and process control. The actual moderate cost of powerful computers converts molecular simulation into an excellent tool to provide predictions of such properties. In particular, the predictive capability of molecular simulation techniques becomes very important when dealing with extreme conditions of temperature and pressure as well as when toxic compounds are involved in the systems to be studied due to the fact that experimentation at such extreme conditions is difficult and expensive.<br/>Consequently, alternative processes must be considered in order to obtain the required properties. Chemical and petrochemical industries have made intensive use of thermophysical models including equations of state, activity coefficients models and corresponding state theories. These predictions present the advantage of providing good approximations with minimal computational needs. However, these models are often inadequate when only a limited amount of information is available to determine the necesary parameters, or when trying to reproduce complex fluid properties such as that of molecules which exhibit hydrogen bonding, polymers, etc. In addition, there is no way for dynamical properties to be estimated in a consistent manner.<br/>In this thesis, the HR and FSS techniques are combined with the main goal of extending the application of these methodologies to the calculation of the vaporliquid equilibrium and critical point of real mixtures. Before applying the methodologies to the real mixtures of industrial interest, the LennardJones fluid has been taken as a reference model and as a preliminary step. In this case, the predictions are affected only by the omnipresent statistical errors, but not by the accuracy of the model chosen to reproduce the behavior of the real molecules or the interatomic potential used to calculate the configurational energy of the system.<br/>The simulations have been performed in the grand canonical ensemble (GCMC)using the GIBBS code. Liquidvapor coexistences curves have been obtained from HR techniques for pure fluids and binary mixtures, while critical parameters were obtained from FSS in order to close the phase envelope of the phase diagrams. In order to extend the calculations to multicomponent systems modifications to the conventional HR techniques have been introduced in order to avoid the construction of histograms and the consequent need for large memory resources. In addition an alternative methodology known as the fourth order cumulant calculation, also known as the Binder parameter, has been implemented to make the location of the critical point more straightforward. In particular, we propose the use of the fourth order cumulant calculation considering two different possibilities: either the intersection of the Binder parameter for two different system sizes or the intersection of the Binder parameter with the known value for the system universality class combined with a FSS study. The development of transferable potential models able to describe the inter and intramolecular energies of the molecules involved in the simulations constitutes an important field in the improvement of Monte Carlo techniques. In the last decade, potential models, also referred to as force fields, have been developed for a wide range of compounds. One of the most common approaches for modeling hydrocarbons and other flexible molecules is the use of the unitedatoms model, where each chemical group is represented by one LennardJones center. This scheme results in a significant reduction of the computational time as compared to allatoms models since the number of pair interactions goes as the square of the number of sites. Improvements on the standard unitedatoms model, where typically a 612 LennardJones center of force is placed on top of the most significant atom, have been proposed. For instance, the AUA model consists of a displacement of the LennardJones centers of force towards the hydrogen atoms, converting the distance of displacement into a third adjustable parameter. In this thesis we have developed AUA 4 intermolecular potentials for three different families of compounds. The family of ethers is of great importance due to their applications as solvents. The other two families, thiophenes and alkanols, play an important roles in the oil and gas industry. Thiophene due to current and future environmental restrictions and alkanols due ever higher importance and presence of biofuels in this industry.

In this thesis, we explore some of the exciting physics of condensed matter systems manifested because of imperfection or disorder and interactions among the constituent particles. In phenomena like transport, e.g., electrical current; localization, e.g., confinement of electrons only within a small part of a system; entanglement (a correlation among the constituents particle); disorder and interaction play essential roles. These three properties are our main focus in the thesis. There are six chapters. In the first chapter, we introduce a few landmarks in the field to set the stage and give an overview of the works presented in the thesis. In the second chapter, we consider quasi-disordered or quasiperiodic systems in one, two, and three dimensions, where the quasi-disorder is deterministic but non-repeating throughout a lattice and considered from. Metal-insulator transitions in these systems are probed by calculating conductances and their change with system size. More specifically, we look at the systems from the perspective of single-parameter scaling theory. In the third chapter, we consider both the disordered and quasi-disordered systems with interactions. The systems show transitions from thermal to many-body localized phases, and we study them in Fock space, which is a natural description for an interacting system. We exploit the Fock space structure to calculate the propagator or Green’s function in an iterative way to push the system size accessible in the exact calculations. We define a length scale in Fock space, which can detect the phase transition and distinguish between the disordered and the quasi-disordered systems. In the fourth chapter, motivated by an experiment, we study the electrical current and noise therein in a disordered quantum Hall system in the proximity of a superconductor. To our surprise, the quantum Hall conductance plateau in the system comes with noise in the current as also observed in the experiment, and the calculated quantities match pretty well with the observed values. In the fifth chapter, we study the entanglement entropy of an interacting fermionic system using a new saddle-point approximation similar to a mean-field approximation. The approximation is based on a newly developed path integral approach for calculating the entanglement entropy. In the last chapter, we conclude the thesis by summarizing the important findings of our works presented in the thesis with some future directions.

This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted to this metric. The chapter has two major themes. The first is a more general reprise of the trichotomy described in Chapter 1 (Theorem 2.0.29). The second theme is a generalization of the fact that Euclidean singular integral operators are closely related to elliptic partial differential equations. The chapter also introduces a quantitative version of the classical Frobenius theorem from differential geometry. This “quantitative Frobenius theorem” can be thought of as yielding “scaling maps” which are well adapted to the Carnot–Carathéodory geometry, and is of central use throughout the rest of the monograph.

This chapter develops the theory of multi-parameter Carnot–Carathéodory geometry, which is needed to study singular integral operators. In the case when the balls are of product type, all of the results are simple variants of results in the single-parameter theory. When the balls are not of product type, these ideas become more difficult. What saves the day is the quantitative Frobenius theorem given in Chapter 2. This can be used to estimate certain integrals, as well as develop an appropriate maximal function and an appropriate Littlewood–Paley square function, all of which are essential to our study of singular integral operators.

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

In Chapter 13, it was shown that the complexity of the LBE collision operator can be cut down dramatically by formulating discrete versions with prescribed local equilibria. In this chapter, the process is taken one step further by presenting a minimal formulation whereby the collision matrix is reduced to the identity, upfronted by a single relaxation parameter, fixing the viscosity of the lattice fluid. The idea is patterned after the celebrated Bhatnagar–Gross–Krook (BGK) model Boltzmann introduced in continuum kinetic theory as early as 1954. The second part of the chapter describes the comeback of the early LBE in optimized multi-relaxation form, as well as few recent variants hereof.

The chapter is a mini outlook on the field. The classic achievenments in complexity science are mentioned, and we summarize how the new directions contained in this book might open new doors into a truly twenty-first-century science of complex systems.We do that by clarifying the origin of scaling laws, in particular for driven non-equilibrium systems, deriving the statistics of driven systems on the basis of driving and relaxing processes, categorizing probabilistic complex systems into universality classes, by developing ways for meaningful generalizations of statistical mechanics, and information theory so that they become useful for complex systems, and finally, by unifying the different approaches to evolution and co-evolution into a single mathematical framework that can serve as the basis for understanding co-evolutionary dynamics of states and interactions. We comment on our view of the role of artificial intelligence and our opinion on the future of science of complex systems.

This book presents a theory of temporal structure for music, making two main arguments. The first is that a single model of temporal structure, expressible in the form of a certain type of mathematical network, is common to all modalities, particularly rhythm, tonality, and form. As a result, we can develop tools to talk about the experience of musical time in abstraction from any particular modality, and make analogies from structural phenomena in one modality to another (e.g., formal counterpoint). The second argument is that each of these modalities is in principle independent: it has its own set of structuring criteria, and it may lead to structures that agree or disagree with each other. The resulting coordination or disjunction between modalities is of more direct aesthetic importance, typically, than anything that can be said about one isolated parameter alone. These claims have deep ramifications for theories of rhythm, tonality, and form: for instance, that it is possible to discuss formal structure without necessary reference to tonal features. Theories of harmony, key, formal function, hypermeter, and closure are developed in conjunction with analysis of a wide range of eighteenth- and nineteenth-century composers, surveys of classical repertoire, and observations about the history of musical styles. A number of mathematical tools for temporal structure are also proposed.

AbstractIn this chapter, we theoretically design bilayer thermoelectric metamaterials based on the generalized scattering-cancellation method. By solving the governing equations directly, we formulate the specific parameter requirements for desired functionalities beyond existing single-field or decoupled multi-field Laplacian metamaterials. Unlike the recently reported transformation thermoelectric flows, bilayer schemes do not require inhomogeneity and anisotropy in constitutive materials. Finite-element simulations confirm the analytical results and show robustness under various exterior conditions. Feasible experimental design with naturally occurring materials is also proposed for further proof-of-principle verification. Our theoretical method may be extended to other coupled multiphysical systems such as thermo-optics, thermomagnetics, and optomechanics.

The major drawbacks of basic electronic components i.e., Vacuum Tubes used before the 1960s were a large size and the inability of these to be scaled down further. With the emphasis shifting to scaling down we came across the MOSFETs in single-gate configuration since the 1960s, they are utilized nowadays in the nanometer region for keeping the high-performance level but still, these single-gate configurations of MOSFETs suffer from different parameters such as coupling, interfacing, channel mobility, channel orientation, switching delay, latch-up and leakage current, short channel effects (DIBL, GIDL, subthreshold swing) and volume inversion and this has led to decrease in inversion charge, increase in leakage current and reduction in the drive current leads us to the exploration of the double-gate configuration of MOSFET and on further exploration it leads us to the novel and higher mobility channel materials such as Si1-xGex which can perform and even shows better results than prevailing single-gate MOSFETs. This paper analyses the different configurations of Si1-xGex for double-gate configuration of MOSFETs and its Future Applications.

Time evolution, near a phase transition in the critical domain of critical systems not far from equilibrium, using a Langevin-type evolution is studied. Typical quantities of interest are relaxation rates towards equilibrium, time-dependent correlation functions and transport coefficients. The main motivation for such a study is that, in systems in which the dynamics is local (on short time-scales, a modification of a dynamic variable has an influence only locally in space) when the correlation length becomes large, a large time-scale emerges, which characterizes the rate of time evolution. This phenomenon called critical slowing down leads to universal behaviour and scaling laws for time-dependent quantities. In contrast with the situation in static critical phenomena, there is no clean and systematic derivation of the dynamical equations governing the time evolution in the critical domain, because often the time evolution is influenced by conservation laws involving the order parameter, or other variables like energy, momentum, angular momentum, currents and so on. Indeed, the equilibrium distribution does not determine the driving force in the Langevin equation, but only the dissipative couplings are generated by the derivative of the equilibrium Hamiltonian, and directly related to the static properties. The purely dissipative Langevin equation specifically discussed, corresponding to static models like the f⁴ field theory and two-dimensional models. Renormalization group (RG) equations are derived, and dynamical scaling relations established.

Abstract This chapter continues the analysis of seasonal competition, begun in Chapter 8. It examines cases in which there are differences in the shapes of two consumer species’ demographic responses (functional and/or numerical response) to resource abundance. Temporal variation affects parameters other than the consumer’s per capita resource capture rate, including variation in the resource growth rate or in a neutral parameter of one or both consumers. As in Chapter 8, temporal variation can make exclusion either more or less likely depending on the details of the mechanism(s) driving that variation. Mutual invasibility of single consumer systems is often not required for coexistence. Alternative attractors are a frequent occurrence in these systems, and different period lengths of temporal environmental variation can result in qualitatively different effects on coexistence. The complicated outcomes are largely due to interaction of the environmental seasonality with the inherent periodicity of one or both consumer–resource interactions.

The chapter analyzes differential flatness theory for the control of single asset and multi-asset option price dynamics, described by PDE models. Through these control methods, stabilization of distributed parameter (PDE modelled) financial systems is achieved and convergence to specific financial performance indexes is made possible. The main financial model used in the chapter is the Black-Scholes PDE. By applying semi-discretization and a finite differences scheme the single-asset (equivalently multi-asset) Black-Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations it is shown that differential flatness properties hold. This enables to solve the associated control problem and to stabilize the options' dynamics. By showing the feasibility of control of the single-asset (equivalently multi-asset) Black-Scholes PDE it is proven that through selected purchases and sales during the trading procedure, the price of options can be made to converge and stabilize at specific reference values.

The chapter analyzes differential flatness theory for the control of single asset and multi-asset option price dynamics, described by PDE models. Through these control methods, stabilization of distributed parameter (PDE modelled) financial systems is achieved and convergence to specific financial performance indices are made possible. The main financial model used in the chapter is the Black-Scholes PDE. By applying semi-discretization and a finite differences scheme the single-asset (equivalently multi-asset) Black-Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations, it is shown that differential flatness properties hold. This enables one to solve the associated control problem and to stabilize the options' dynamics. By showing the feasibility of control of the single-asset (equivalently multi-asset) Black-Scholes PDE, it is proven that through selected purchases and sales during the trading procedure, the price of options can be made to converge and stabilize at specific reference values.

Prior analyses and experiments have demonstrated that varying or scaling the number of fluid channels in each layer of a stacked multi-layer heat sink yields distinct advantages over traditional single-layer designs which use channels with high aspect ratios. Specifically, a design which implements scaling in order to vary the porosity (or equivalently, the number of channels) from one layer to the next allows a given thermal performance to be realized at a lower pressure drop than the corresponding non-scaled design. While previous studies use porous media theory for their analytical foundation just as the current studies do, they also focused on heat exchangers with machined channels, and have consequently been limited to discrete variation of the porosity (or number of channels) in each layer. Extending this approach by allowing for continuous porosity variation provides a generalized and powerful design method for scaled multi-layer heat exchangers by mathematically modeling them using two-equation volume averaged quantities. This approach also yields insight into the fundamental design parameters which control the performance of this class of heat exchangers, and suggests that their performance-governing parameters are similar to those which govern fin performance. This paper focuses primarily on the thermal behavior of these liquid cooled heat sinks which employ various scaling functions to define the spatial variation of porosity. Comparisons are made with available closed-form solutions as well as results available from prior studies of discretely-scaled designs. The results indicate that scaling laws which have not been investigated previously can likely yield further performance improvements relative to prior designs.

Abstract An increasingly common experimental technique allows measurement of overall effectiveness by matching the Biot number between experimental and engine conditions. The measured overall effectiveness distribution correlates to the expected turbine component temperature distribution. While a good deal of work has been devoted to determining the appropriate flow conditions necessary to scale adiabatic effectiveness, very little attention has been paid to the subtleties beyond matching the Biot number that arise when performing experiments on a conducting model to determine overall effectiveness. Notably, the ratio of the internal and external heat transfer coefficient must be matched. The density ratio and more recently, the specific heat ratio, have been shown to play important roles in scaling adiabatic effectiveness; however, in the present work, we demonstrate the requirements for the coolant and freestream flow conditions required to conduct an appropriately scaled overall effectiveness experiment. Since the viscosity and thermal conductivity of the fluids (in addition to density and specific heat) play significant roles that influence heat transfer coefficient behavior, this gives rise to an additional nondimensional parameter that should, in theory, be matched to properly execute an overall effectiveness experiment. In this paper, we demonstrate that this new nondimensional parameter will be matched provided that Pr∞, Prc, and Rec are matched in addition to the freestream Reynolds number and the advective capacity ratio. We demonstrate the validity of this requirement through computational fluid dynamics simulations, which are well-suited for this since the over-constrained requirements can be overcome by altering gas properties from the real values. Simulations of an internally cooled wall exposed to a hot freestream were performed with various gases to show the sensitivity of the overall effectiveness to these previously ignored requirements. An additional set of simulations on a film cooled plate reveals additional complexities when coolant mixes with the freestream gas.

Abstract Effective design of film cooled engine components requires the ability to predict behavior at engine conditions. This is commonly accomplished through low temperature testing on scaled up geometries. The adiabatic effectiveness, η, is one indicator of the performance of a film cooling scheme. Performing an experiment to measure η in a low temperature wind tunnel requires appropriate selection of the coolant flow rate. Perhaps the most common flow rate parameter that is used to characterize the coolant flow relative to the freestream is the mass flux ratio, or blowing ratio, M. This is usually used in lieu of the velocity ratio to account for the fact that the density of the coolant is typically much larger than that of the hot freestream gas. Numerous studies have taken place evaluating the ability of M to properly scale the effects of density ratio and its performance has produced mixed results. The momentum flux ratio, I, is an alternative that is also found to have mixed success, leading some to recommend matching the density ratio to allow simultaneous matching of M and I. Nevertheless, widely varying results in the literature regarding the efficacy of these coolant flow rate parameters to scale the density ratio suggests there may be other largely ignored effects playing a role in the thermal physics. In the present work, thermal experiments were performed to measure adiabatic effectiveness on a flat plate with a single 7-7-7 shaped hole. Various coolant gases were used to give a large range of thermodynamic property variations. It is shown that a relatively new coolant flow rate parameter that accounts for not only density variations but also specific heat variations, the advective capacity ratio (ACR), far exceeds the ability of either M or I to provide matched adiabatic effectiveness between the various coolant gases that exhibit extreme property differences. Particularly considering that the specific heat of the coolant in an engine is significantly lower than the specific heat of the freestream gas, ACR is shown to be appropriate for characterizing non-separating coolant flow situations.

A new set of experiments have been performed in order to study the effects of the upstream conditions and the surface roughness on a zero pressure gradient turbulent boundary layer. In order to properly capture the x-dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed. These 2-D Laser Doppler Anemometry (LDA) measurements enable us to use the full boundary layer equations in order to calculate the skin friction and determine the boundary layer development which is not possible in the majority of experiments on rough surfaces. It will be shown that for fixed experimental conditions (i.e., fixed upstream wind tunnel speed, trip wire, etc), the velocity deficit profiles collapse for each of the scalings investigated but only the Zagarola/Smits scaling (1998) could collapse all the different experimental conditions into a single curve. In addition, the Reynolds stresses were increasingly affected by the surface roughness as the roughness parameter, k+, increased. Moreover, it was found that the shape of the Reynolds stress profiles was very different throughout the entire boundary layer, particularly the &lt; u2 &gt; component. This is likely the result of the flow becoming more isotropic for increased k+, and will be seen in the anisotropy coefficients. Moreover, increased production of &lt; u2 &gt; and &lt; uv &gt; due to roughness is also seen throughout the entire boundary layer although its overall role in the changing shape of the &lt; u2 &gt; profiles still needs to be determined. The effect of roughness on the boundary layer parameters is also evident and their x-dependence is also shown.

Abstract The bridge between the multibody dynamic modeling theory and nonlinear dynamic analysis theory is built for the first time in this work by introducing an efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method for steady-state nonlinear dynamic analysis of index-3 differential algebraic equations (DAEs) for general rigid multibody systems. The multibody dynamic modeling theory has made significant advances in generality and simplicity, and multibody systems are usually governed by DAEs. Since the fast Fourier transform and EGA are used, the EGA-IHB method has excellent robustness and computational efficiency. Since the Floquet theory cannot be directly used for stability analysis of periodic responses of DAEs, a new stability analysis procedure is developed, where perturbed, linearized DAEs are reduced to ordinary differential equations with use of independent generalized coordinates. A modified arc-length continuation method with a scaling strategy is used for calculating response curves and conducting parameter studies. Three examples are used to show the performance and capability of the current method. Periodic solutions of DAEs from the EGA-IHB method show excellent agreement with those from numerical integration methods. Amplitude-frequency and amplitude-parameter response curves are generated, and stability and period-doubling bifurcations are analyzed. The EGA-IHB method can be used as a universal solver and nonlinear analyzer for obtaining steady-state periodic responses of DAEs for general multibody systems.

Abstract An improved understanding of the failure behaviour of safety critical component could result in substantial benefits for industry; these include a reduction in design constraints resulting in optimised and cheaper designs, reduced risk and therefore cost. Yet surprisingly, there is little information in design and assessment codes on the behaviour of thin sections. The aim of this paper is to investigate the fracture of thin sections, with reduced out-of-plane plastic constraint, by using a unified measure of constraint. A range of single edge notched bend specimen made of stainless steel 316L were tested. The specimens had a combination of in-plane and out-of-plane constraint levels achieved through different crack lengths and thicknesses. FEA simulations of the tested specimens were conducted to estimate the crack tip stress and strain fields for each, in order to determine Rice and Tracey contour values. Using critical values of Rice and Tracey parameter and a critical area (normalised by thickness) enclosed by this parameter, toughness scaling values for low constraint specimens are calculated.

Abstract Software with a user-friendly interface is presented for integrating energy storage and renewable energy sources with co-generation and tri-generation (CHP) systems. This simulation provides a first level screening of CHP systems and determines the effects of including renewable energy or storage systems. The inputs consist of the application’s electric load and thermal load as well as the parameters for the power producing devices, back up boilers/furnaces, vapor compression refrigeration COP and the generator and inverter efficiency. The output is the energy utilization factor (EUF), the rates of carbon dioxide production and entropy production. The simulation is based on using the thermal load to power ratio, HLRP, as a basic scaling parameter and the ratio of the cooling to total thermal load, CHR. A single design point investigation or continuous load information as well as the renewable energy output and energy storage data is controlled by the user. A dashboard report and an excel format is provided to allow the user to perform their own detail summary of the calculated results. Results comparing the performance of a CHP plant for different applications are provided. As expected, the CHP device outperforms the traditional means producing electricity.

Long-range guided wave pipeline inspection is claimed to be able to inspect ranges of well over 30 meters (100 Feet) in either direction (i.e. total inspection greater than 60 Meters or 200 Ft.) from a single position. In terms of inspected meters per measurement and cost per meter this technique can be a fundamental improvement from conventional methods for pipeline inspection. For inspection of hard-to-access locations it offers a good on-stream screening alternative by being able to image the pipe section from an easier-access location. Examples of inaccessible locations are road-, railway-, river-, dike- and other crossings. Excavating the pipeline for inspection at these locations is expensive and the potential cost savings of a technique like long-range pipeline inspection are attractive. The objective of this project was to combine theory, modeling and experimental/operational elements in order to be able to handle the more complex situations as found at buried sections of pipelines, more specifically bitumen coating. Laboratory and field experiments supported by modeling and developing an approach to inspect a coated pipe configuration are parts of this work in order to get both reliable and practical knowledge. Another important part was the evaluation of the different transducer and equipment concepts available and establish their merits. In the project the propagation and reflection of guided waves was modeled and simulated for relevant situations. Two suppliers, SwRI and PiL, were involved in laboratory trials and field trials both to confirm the modeling and obtain a clear view of the practical aspects in operation and the actual capabilities of their systems. Modeling resulted in a formula providing estimates for the reflectivity of defects. Using scaling rules these were compared to data obtained in the laboratory trials.

Surface area of glaciers and perennial snow within Mount Rainier National Park were delineated based on 2021 aerial Structure-from-Motion (SfM) and satellite imagery to document changes to glaciers over the last 125 years. These extents were compared with previously completed databases from 1896, 1913, 1971, 1994, 2009, and 2015. In addition to the glacial features mapped at the Park, any snow patches noted in satellite- and fixed-wing- acquired aerial images in September 2021 were mapped as perennial snowfields. In 2021, Mount Rainier National Park contained a total of 28 named glaciers which covered a total of 75.496 ± 4.109 km2 (29.149 ± 1.587 mi2). Perennial snowfields added another 1.938 ± 0.112 km2 (0.748 ± 0.043 mi2), bringing the total perennial snow and glacier cover within the Park in 2021 to 77.434 ± 4.221 km2 (29.897 ± 1.630 mi2). The largest glacier at Mount Rainier was the Emmons Glacier, which encompasses 10.959 ± 0.575 km2 (4.231 ± 0.222 mi2). The change in glacial area from 1896 to 2021 was -53.812 km2 (-20.777 mi2), a total reduction of 41.6%. This corresponds to an average rate of -0.430 km2 per year (-0.166 mi2 × yr-1) during the 125 year period. Recent changes (between the 6-year period of 2015 to 2021) showed a reduction of 3.262 km2 (-1.260 mi2) of glacial area, or a 4.14% reduction at a rate of -0.544 km2 per year ( 0.210 mi2 × yr-1). This rate is 2.23 times that estimated in 2015 (2009-2015) of -0.244 km2 per year (-0.094 mi2 × yr-1). Changes in ice volume at Mount Rainier and estimates of total volumes were calculated for 1896, 1913, 1971, 1994, 2009, 2015, and 2021. Volume change between 1971 and 2007/8 was -0.65 km3 ( 0.16 mi3; Sisson et al., 2011). We used the 2007/8 LiDAR digital elevation model and our 2021 SfM digital surface model to estimate a further loss of -0.404 km3 (-0.097 mi3). In the 50-year period between 1971 and 2021, the glaciers and perennial snowfields of Mount Rainier lost a total of -1.058 km3 (-0.254 mi3) at a rate of -0.021 km3 per year (-0.005 mi3 × yr-1). The calculation of the total volume of the glaciers during various glacier extent inventories at Mount Rainier is not straightforward and various methods are explored in this paper. Using back calculated scaling parameters derived from a single volume measurement in 1971 and estimates completed by other authors, we have developed an estimate of glacial mass during the last 125-years at Mount Rainier that mostly agree with volumetric changes observed in the last 50 years. Because of the high uncertainty with these methods, a relatively modest 35% error is chosen. In 2021, Mount Rainier’s 28 glaciers contain about 3.516 ± 1.231 km3 (0.844 ± 0.295 mi3) of glacial ice, snow, and firn. The change in glacial mass over the 125-year period from 1896 to 2021 was 3.742 km3 (-0.898 mi3), a total reduction of 51.6%, at an average rate of -0.030 km3 per year ( 0.007 mi3 × yr-1). Volume change over the 6-year period of 2015 to 2021 was 0.175 km3 (-0.042 mi3), or a 4.75% reduction, at a rate of -0.029 km3 per year (-0.007 mi3 × yr-1). This survey officially removes one glacier from the Park’s inventory and highlights several other glaciers in a critical state. The Stevens Glacier, an offshoot of the Paradise Glacier on the Park’s south face, was removed due to its lack of features indicating flow, and therefore is no longer a glacier but instead a perennial snowfield. Two other south facing glaciers – the Pyramid and Van Trump glaciers – are in serious peril. In the six-year period between 2015 and 2021, these two glaciers lost 32.9% and 33.6% of their area and 42.0% and 42.9% of their volume, respectively. These glaciers are also becoming exceedingly fragmented and no longer possess what can be called a main body of ice. Continued losses will quickly lead to the demise of these glaciers in the coming decades. Overall, the glaciers on the south face of the mountain have been rapidly shrinking over the last 125 years. Our data shows a continuation of gradual yet accelerating loss of glacial ice at Mount Rainier, resulting in significant changes in regional ice volume over the last century. The long-term impacts of this loss will be widespread and impact many facets of the Park ecosystem. Additionally, rapidly retreating south-facing glaciers are exposing large areas of loose sediment that can be mobilized to proglacial rivers during rainstorms, outburst floods, and debris flows. Regional climate change is affecting all glaciers at Mount Rainier, but especially those smaller cirque glaciers and discontinuous glaciers on the south side of the volcano. If the regional climate trend continues, further loss in glacial area and volume parkwide is anticipated, as well as the complete loss of small glaciers at lower elevations with surface areas less than 0.2 km2 (0.08 mi2) in the next few decades.