Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

I. A seismotectonic study of the Middle America Subduction Zone. II. Lithosphere and upper mantle structure of the Canadian Shield and Eastern North America

This thesis consists of two separate parts. Part I (Chapter 1) is concerned with seismotectonics of the Middle America subduction zone. In this chapter, stress distribution and Benioff zone geometry are investigated along almost 2000 km of this subduction zone, from the Rivera Fracture Zone in the north to Guatemala in the south. Particular emphasis is placed on the effects on stress distribution of two aseismic ridges, the Tehuantepec Ridge and the Orozco Fracture Zone, which subduct at seismic gaps. Stress distribution is determined by studying seismicity distribution, and by analysis of 190 focal mechanisms, both new and previously published, which are collected here. In addition, two recent large earthquakes that have occurred near the Tehuantepec Ridge and the Orozco Fracture Zone are discussed in more detail. A consistent stress release pattern is found along most of the Middle America subduction zone: thrust events at shallow depths, followed down-dip by an area of low seismic activity, followed by a zone of normal events at over 175 km from the trench and 60 km depth. The zone of low activity is interpreted as showing decoupling of the plates, and the zone of normal activity as showing the breakup of the descending plate. The portion of subducted lithosphere containing the Orozco Fracture Zone does not differ significantly, in Benioff zone geometry or in stress distribution, from adjoining segments. The Playa Azul earthquake of October 25, 1981, M_s=7.3, occurred in this area. Body and surface wave analysis of this event shows a simple source with a shallow thrust mechanism and gives M_o=1.3x10²⁷ dyne-cm. A stress drop of about 45 bars is calculated; this is slightly higher than that of other thrust events in this subduction zone. In the Tehuantepec Ridge area, only minor differences in stress distribution are seen relative to adjoining segments. For both ridges, the only major difference from adjoining areas is the infrequency or lack of occurrence of large interplate thrust events.

Part II involves upper mantle P wave structure studies, for the Canadian shield and eastern North America. In Chapter 2, the P wave structure of the Canadian shield is determined through forward waveform modeling of the phases P_nl, P, and PP. Effects of lateral heterogeneity are kept to a minimum by using earthquakes just outside the shield as sources, with propagation paths largely within the shield. Previous mantle structure studies have used recordings of P waves in the upper mantle triplication range of 15-30°; however, the lack of large earthquakes in the shield region makes compilation of a complete P wave dataset difficult. By using the phase PP, which undergoes triplications at 30-60°, much more information becomes available. The WKBJ technique is used to calculate synthetic seismograms for PP, and these records are modeled almost as well as the P. A new velocity model, designated S25, is proposed for the Canadian shield. This model contains a thick, high-Q, high-velocity lid to 165 km and a deep low-velocity zone. These features combine to produce seismograms that are markedly different from those generated by other shield structure models. The upper mantle discontinuities in S25 are placed at 405 and 660 km, with a simple linear gradient in velocity between them. Details of the shape of the discontinuities are not well constrained. Below 405 km, this model is not very different from many proposed P wave models for both shield and tectonic regions.

Chapter 3 looks in more detail at recordings of P_nl in eastern North America. First, seismograms from four eastern North American earthquakes are analyzed, and seismic moments for the events are calculated. These earthquakes are important in that they are among the largest to have occurred in eastern North America in the last thirty years, yet in some cases were not large enough to produce many good long-period teleseismic records. A simple layer-over-a-halfspace model is used for the initial modeling, and is found to provide an excellent fit for many features of the observed waveforms. The effects on P_nl of varying lid structure are then investigated. A thick lid with a positive gradient in velocity, such as that proposed for the Canadian shield in Chapter 2, will have a pronounced effect on the waveforms, beginning at distances of 800 or 900 km. P_nl records from the same eastern North American events are recalculated for several lid structure models, to survey what kinds of variations might be seen. For several records it is possible to see likely effects of lid structure in the data. However, the dataset is too sparse to make any general observations about variations in lid structure. This type of modeling is expected to be important in the future, as the analysis is extended to more recent eastern North American events, and as broadband instruments make more high-quality regional recordings available.

Computational Predictions of G Protein-Coupled Receptor Structures and Binding Sites

G protein-coupled receptors (GPCRs) are the largest family of proteins within the human genome. They consist of seven transmembrane (TM) helices, with a N-terminal region of varying length and structure on the extracellular side, and a C-terminus on the intracellular side. GPCRs are involved in transmitting extracellular signals to cells, and as such are crucial drug targets. Designing pharmaceuticals to target GPCRs is greatly aided by full-atom structural information of the proteins. In particular, the TM region of GPCRs is where small molecule ligands (much more bioavailable than peptide ligands) typically bind to the receptors. In recent years nearly thirty distinct GPCR TM regions have been crystallized. However, there are more than 1,000 GPCRs, leaving the vast majority of GPCRs with limited structural information. Additionally, GPCRs are known to exist in a myriad of conformational states in the body, rendering the static x-ray crystal structures an incomplete reflection of GPCR structures. In order to obtain an ensemble of GPCR structures, we have developed the GEnSeMBLE procedure to rapidly sample a large number of variations of GPCR helix rotations and tilts. The lowest energy GEnSeMBLE structures are then docked to small molecule ligands and optimized. The GPCR family consists of five subfamilies with little to no sequence homology between them: class A, B1, B2, C, and Frizzled/Taste2. Almost all of the GPCR crystal structures have been of class A GPCRs, and much is known about their conserved interactions and binding sites. In this work we particularly focus on class B1 GPCRs, and aim to understand that family’s interactions and binding sites both to small molecules and their native peptide ligands. Specifically, we predict the full atom structure and peptide binding site of the glucagon-like peptide receptor and the TM region and small molecule binding sites for eight other class B1 GPCRs: CALRL, CRFR1, GIPR, GLR, PACR, PTH1R, VIPR1, and VIPR2. Our class B1 work reveals multiple conserved interactions across the B1 subfamily as well as a consistent small molecule binding site centrally located in the TM bundle. Both the interactions and the binding sites are distinct from those seen in the more well-characterized class A GPCRs, and as such our work provides a strong starting point for drug design targeting class B1 proteins. We also predict the full structure of CXCR4 bound to a small molecule, a class A GPCR that was not closely related to any of the class A GPCRs at the time of the work.

I. A study of the dynamics of triplet excitons in molecular crystals. II. An investigation of delayed light emission from Chlorella pyrenoidosa

I. PREAMBLE AND SCOPE

Brief introductory remarks, together with a definition of the scope of the material discussed in the thesis, are given.

II. A STUDY OF THE DYNAMICS OF TRIPLET EXCITONS IN MOLECULAR CRYSTALS

Phosphorescence spectra of pure crystalline naphthalene at room temperature and at 77˚ K are presented. The lifetime of the lowest triplet ³B_1u state of the crystal is determined from measurements of the time-dependence of the phosphorescence decay after termination of the excitation light. The fact that this lifetime is considerably shorter in the pure crystal at room temperature than in isotopic mixed crystals at 4.2˚ K is discussed, with special importance being attached to the mobility of triplet excitons in the pure crystal.

Excitation spectra of the delayed fluorescence and phosphorescence from crystalline naphthalene and anthracene are also presented. The equation governing the time- and spatial-dependence of the triplet exciton concentration in the crystal is discussed, along with several approximate equations obtained from the general equation under certain simplifying assumptions. The influence of triplet exciton diffusion on the observed excitation spectra and the possibility of using the latter to investigate the former is also considered. Calculations of the delayed fluorescence and phosphorescence excitation spectra of crystalline naphthalene are described.

A search for absorption of additional light quanta by triplet excitons in naphthalene and anthracene crystals failed to produce any evidence for the phenomenon. This apparent absence of triplet-triplet absorption in pure crystals is attributed to a low steady-state triplet concentration, due to processes like triplet-triplet annihilation, resulting in an absorption too weak to be detected with the apparatus used in the experiments. A comparison of triplet-triplet absorption by naphthalene in a glass at 77˚ K with that by naphthalene-h₈ in naphthalene-d₈ at 4.2˚ K is given. A broad absorption in the isotopic mixed crystal triplet-triplet spectrum has been tentatively interpreted in terms of coupling between the guest ³B_1u state and the conduction band and charge-transfer states of the host crystal.

III. AN INVESTIGATION OF DELAYED LIGHT EMISSION FROM Chlorella Pyrenoidosa

An apparatus capable of measuring emission lifetimes in the range 5 X 10^-9 sec to 6 X 10^-3 sec is described in detail. A cw argon ion laser beam, interrupted periodically by means of an electro-optic shutter, serves as the excitation source. Rapid sampling techniques coupled with signal averaging and digital data acquisition comprise the sensitive detection and readout portion of the apparatus. The capabilities of the equipment are adequately demonstrated by the results of a determination of the fluorescence lifetime of 5, 6, 11, 12-tetraphenyl-naphthacene in benzene solution at room temperature. Details of numerical methods used in the final data reduction are also described.

The results of preliminary measurements of delayed light emission from Chlorella Pyrenoidosa in the range 10^-3 sec to 1 sec are presented. Effects on the emission of an inhibitor and of variations in the excitation light intensity have been investigated. Kinetic analysis of the emission decay curves obtained under these various experimental conditions indicate that in the millisecond-to-second time interval the decay is adequately described by the sum of two first-order decay processes. The values of the time constants of these processes appear to be sensitive both to added inhibitor and to excitation light intensity.

Dielectric recovery of short A-C arcs between low-boiling-point electrodes

The re-ignition characteristics (variation of re-ignition voltage with time after current zero) of short alternating current arcs between plane brass electrodes in air were studied by observing the average re-ignition voltages on the screen of a cathode-ray oscilloscope and controlling the rates of rise of voltage by varying the shunting capacitance and hence the natural period of oscillation of the reactors used to limit the current. The shape of these characteristics and the effects on them of varying the electrode separation, air pressure, and current strength were determined.

The results show that short arc spaces recover dielectric strength in two distinct stages. The first stage agrees in shape and magnitude with a previously developed theory that all voltage is concentrated across a partially deionized space charge layer which increases its breakdown voltage with diminishing density of ionization in the field-tree space. The second stage appears to follow complete deionization by the electric field due to displacement of the field-free region by the space charge layer, its magnitude and shape appearing to be due simply to increase in gas density due to cooling. Temperatures calculated from this second stage and ion densities determined from the first stage by means of the space charge equation and an extrapolation of the temperature curve are consistent with recent measurements of arc value by other methods. Analysis or the decrease with time of the apparent ion density shows that diffusion alone is adequate to explain the results and that volume recombination is not. The effects on the characteristics of variations in the parameters investigated are found to be in accord with previous results and with the theory if deionization mainly by diffusion be assumed.

High- and low-latitude climate interactions: evidence for enhanced aridity of Asian monsoon dust source areas after 2.4 MYR from ODP Leg 117 magnetic susceptibility data

EXTRACT (SEE PDF FOR FULL ABSTRACT): Whole-core magnetic susceptibility can sometimes be used as a rapid and sensitive indicator of variations in the concentration of terrigenous material. We apply this approach to study the evolution of Plio-Pleistocene climatic cycles of terrigenous sedimentation at Ocean Drilling Program Site 721, on the Owen Ridge in the Arabian Sea.

Seasonal resolution of laminated sediments in Santa Barbara Basin: its significance in paleoclimatic studies

Sediments in Santa Barbara Basin contain microfossil and sedimentological information that allows reconstruction of major features of the California Current such as water temperature, strength of upwelling, and productivity. ... Until now, investigations of Santa Barbara Basin sediments have utilized analytical techniques that could not resolve seasonal laminae, permitting annual resolution of variations in sediment composition and structure only. ... Based on a successful technique for preparation of epoxy-embedded and highly polished thin-sections that permit economical optical and electron microscope evaluation of laminated sequences, it is our long-term goal to reconstruct, with unprecedented detail, the history of sedimentation processes in the Santa Barbara Basin by developing ultra-high-resolution time series of biotic and detrital proxies.

Long-term changes and variability of monthly extreme temperatures in India

Extreme temperatures are changing worldwide together with changes in the mean temperatures. This study investigates the long-term trends and variations of the monthly maximum and minimum temperatures and their effects on seasonal fluctuations in various climatological regions in India. The magnitude of the trends and their statistical significance were determined by parametric ordinary least square regression techniques and the variations were determined by the respective coefficient of variations. The results showed that the monthly maximum temperature increased, though unevenly, over the last century. Minimum temperature changes were more variable than maximum temperature changes, both temporally and spatially, with results of lesser significance. The results of this study are good indicators of Indian climate variability and its changes over the last century. © Springer-Verlag 2009.

Effect of starvation on the biochemical composition of Clarias batrachus (Linn.)

Marked changes were observed in different chemical constituents of C. batrachus during starvation. The N and protein fractions showed a definite pattern of variations. The highest values of these were recorded on 10th day of starvation and thereafter values declined gradually. On the other hand, the acid soluble phosphorus exhibited a reverse trend, increasing gradually from the first to the 30th day of starvation. These changes have been attributed mainly to the energy and metabolic demands of the starving fish.

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre-matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.

Gas transport property of homo- and copolyimides from isomeric thiaphthalic dianhydride and oxydianiline

Gas transport properties of home- and copolyimides prepared from 3,3',4,4'- and 2,2',3,3'-thiaphthalic dianhydride (p-TDPA and m-TDPA, respectively) with 4,4-oxydianiline (ODA) were investigated. The fractional free volume of m-TDPA-ODA is larger than that of p-TDPA-ODA, and the chain segmental mobility of the former is lower than that of the latter. The permeability coefficients of m-TDPA-ODA to H-2, CO2, and O-2 are more increased by 48, 69 and 75%, at 30 degrees C and 10 atm, respectively, than those of p-TDPA-ODA; but the permselectivities of m-TDPA-ODA for H-2, CO2, and O-2 toward N-2 are more decreased by 33, 77, and 26%, respectively, than those of p-TDPA-ODA. The permeability coefficients and the diffusion coefficients of the copolyimides can be described by the following equations: log P = Phi(p) log P-p + Phi(m), log P-m and log D-a = D-a = Phi(p) log(D-alpha)(p) + Phi(m) log(D-a)(m), respectively. The variation of the permselectivity is controlled predominantly by diffusivity selectivity. These observations are interpreted in terms of variations in the fractional free volume of polyimides. (C) 1997 John Wiley & Sons, Inc.

TEMPERATURE EFFECT ON IMPACT FRACTURE-TOUGHNESS AND FRACTURE MECHANISM OF PHENOLPHTHALEIN POLY(ETHER KETONE)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K-c and critical strain energy release rate G(c). Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.

SELECTED NINETEENTH CENTURY VARIATIONS FOR PIANO

The beauty and artistry of the variation form were fully developed and represented in the nineteenth century. The treasures of nineteenth century piano variations are a significant part of the total piano repertoire. The main goal of this dissertation is to show how various composers of the nineteenth century used the variation form to project their imagination and coloring of a simple melody. They used many different techniques to vary melodies and create their own music. Beethoven's Piano Sonata No. 12 in A-flat Major Op. 26 breaks with the conventional sonata design by using variation form instead of sonata-allegro form for the first movement, and having no movement in sonata-allegro form. Chopin's Variations Brillantes on "Je Vends des scapulaires" Op. 12 and Henri Herz's Variations on 'Non piu mesta" from "La Cenerentola" shows how they applied their art to composing variations on opera themes. Mendelssohn's Variations Serieuses Op. 54 was a reaction against the salon music in the 19" century. Schubert applies the variation form to his Impromptus in B-flat D. 935 No. 3. Schurnann's Symphonic Etudes represents a perfect example of the arts of variation, using counterpoint, and special coloring; and Faure's Theme and Variations Op. 73 represents one of the most outstanding nineteenth-century works in variation form. As a traditionalist in the nineteenth century, Brahms favored the variations over other classic forms. I have performed three of his most important sets of variations: including Variations on a theme by Schumann Op. 9, Variations on a Theme by Handel Op. 24, and Variations for two pianos on a Theme by Haydn Op. 56b. The variations listed above were divided into three recitals. These variations represent a very important part of the piano music of the nineteenth century. By discovering, preparing, and performing these wonderful works, I have grown, both as a pianist and as a musician.

USE OF VARIATION AND FUGUE IN PIANO MUSIC FOLLOWING THE CLASSICAL PERIOD

The variation and fugue originated from the 15th and 16th centuries and blossomed during the Baroque and Classical Periods. In a variation, a theme with a particular structure precedes a series of pieces that usually have the same or very similar structure. A fugue is a work written in imitative counterpoint in which the theme is stated successively in all voices of polyphonic texture. Beethoven’s use of variation and fugue in large scale works greatly influenced his contemporaries. After the Classical Period, variations continued to be popular, and numerous composers employed the technique in various musical genres. Fugues had pedagogical associations, and by the middle of 19th century became a requirement in conservatory instruction, modeled after Bach’s Well-Tempered Clavier. In the 20th century, the fugue was revived in the spirit of neoclassicism; it was incorporated in sonatas, and sets of preludes and fugues were composed. Schubert's Wanderer Fantasy presents his song Der Wanderer through thematic transformations, including a fugue and a set of variations. Liszt was highly influenced by this, as shown in his thematic transformations and the fugue as one of the transformations in his Sonata in b. In Schumann’s Symphonic Études, Rachmaninoff's Rhapsody on a Theme of Paganini and Copland’s Piano Variations, the variation serves as the basis for the entire work. Prokofiev and Schubert take a different approach in Piano Concerto No. 3 and Wanderer Fantasy, employing the variation in a single movement. Unlike Schubert and Liszt's use of the fugue as a part of the piece or movement, Franck’s Prelude Chorale et Fugue and Shchedrin’s Polyphonic Notebook use it in its independent form. Since the Classical Period, the variation and fugue have evolved from stylistic and technical influences of earlier composers. It is interesting and remarkable to observe the unique effects each had on a particular work. As true and dependable classic forms, they remain popular by offering the composer an organizational framework for musical imagination.

VARIATION FORMS: A SURVEY THROUGH FOUR CENTURIES OF VIOLIN REPERTOIRE

Variation, or the re-working of existing musical material, has consistently attracted the attention of composers and performers throughout the history of Western music. In three recorded recitals at the University of Maryland School of Music, this dissertation project explores a diverse range of expressive possibilities for violin in seven types of variation form in Austro-German works for violin from the 17th through the 20th centuries. The first program, consisting of Baroque Period works, performed on period instrument, includes the divisions on “John come kiss me now” from The Division Violin by Thomas Baltzar (1631 – 1663), constant bass variations in Sonate Unarum Fidium by Johann Heinrich von Schmelzer (1623 – 1680), arbitrary variation in Sonata for Violin and Continuo in E Major, Op. 1, No. 12 “Roger” by George Friedrich Händel (1685 – 1759), and French Double style, melodic-outline variation in Partita for Unaccompanied Violin in B Minor by Johan Sebastian Bach (1685 – 1750). Theme and Variations, a popular Classical Period format, is represented by the Sonata for Piano and Violin in G Major K. 379 by Wolfgang Amadeus Mozart (1756 – 1791) and Sonata for Violin and Piano in A Major, Op. 47 No. 9 the “Kreutzer” by Ludwig van Beethoven (1770 – 1827). Fantasy for Piano and Violin in C Major D. 934 by Franz Schubert (1797 – 1828) represents the 19th century fantasia variation. In these pieces, the piano and violin parts are densely interwoven, having equal importance. Many 20th century composers incorporated diverse types of variations in their works and are represented in the third recital program comprising: serial variation in the Phantasy for Violin and Piano Op.47 of Arnold Schoenberg (1874 – 1951); a strict form of melodic-outline variation in Sonate für Violine allein, Op. 31, No. 2 of Paul Hindemith (1895 – 1963); ostinato variation in Johan Halvorsen’s (1864 – 1935) Passacaglia for Violin and Viola, after G. F. Handel’s Passacaglia from the Harpsichord Suite No. 7 in G Minor. Pianist Audrey Andrist, harpsichordist Sooyoung Jung, and violist Dong-Wook Kim assisted in these performances.