Effects Of Phase Changes Research Articles

Effects of phase shifts on four-beam interference patterns

An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.

Effects of phase changes on weld pool shape in laser welding

A mathematical model is developed to relate the weld depth and width to the laser parameters. The model is based on the Stefan condition for quasi-steady state laser welding. Simple expressions are obtained for the shapes of the solid - liquid and liquid - vapour interfaces. They are found as functions of the laser irradiance, welding speed, absorptivity and thermal diffusivity. Simple expressions for the temperature distributions in the liquid and solid phases are also presented. The results for the weld depths and widths and the temperature distributions in the workpiece are illustrated for various laser intensities and welding speeds. The predictions of this simple model are found to compare well with experimental data and other previous models.

Effects of phase changes on reflection and their wavelength dependence in optical profilometry

The method as well as an appropriate instrumentation for measuring phase changes of reflected light is described. The phase changes on samples of Au, Al, Ag, and Cr evaporated films are measured for five wavelengths (lambda) from 442 to 633 nm, with respect to the phase change at the glass-air interface, where it should be zero. The measured results for the Au film are in fairly good agreement with values calculated by use of optical constants from a handbook or the complex refractive index measured by an ellipsometer. The phase changes for Al and Ag films are different from calculated values by ~5 degrees or a shift length of 4.4 nm at lambda = 633 nm, while those of the Cr film show large shifts as high as 16 degrees or a shift length of 9.8 nm at lambda = 442 nm.

Analysis of Residual Stresses and Metallurgical Phase Changes in Centrifugally Cast Bi-Metal Grinding Rolls

A mathematical model was developed for computing the metallurgical phase transformations and residual stresses in centrifugal casting of bi-metal grinding rolls used for coal pulverizing. The model considers variation of thermo-mechanical properties of material with temperature, effects of phase changes and metallurgical phase transformations. Rolls idealized as having infinite cylindrical geometry and the actual finite conical geometry are analysed for cases of air and water jet cooling of the centrifuging die. As expected an increase in the martensitic fraction is obtained on the grinding surface due to water jet cooling. The study indicates that the large size rolls analysed herein have higher martensitic fraction as compared to small size roll. Simplified analysis model is developed for usage in parametric studies involving various sizes for initial sizing of the rolls.

One dimensional isothermal spinning models for liquid crystalline polymer fibers

A slender one dimensional (1D) model for filaments of liquid crystalline polymers (LCPs) is applied to simulate isothermal fiber spinning of materials with internal orientation. The focus is on the hydrodynamic-orientation interactions in spinning flows, isolated from other significant spinline effects of temperature, crystallization, and phase changes. Spun fiber orientation (in particular, birefringence) is deduced from first principles along with fiber diameter and velocity. One result of our modeling and simulations is that, in isothermal spinning, the microstructure (orientation tensor) is weakly radially dependent and can be calculated from 1D models. Families of numerical steady state fiber spinning solutions, together with their linearized stability, are presented. These calculations reveal upper bounds on throughput in terms of the critical draw ratio, above which the process is unstable. The effects on stability due to LCP parameter changes are thoroughly investigated. We find enhancement of the...

Quantitative modelling of the Tunguska Basin evolution in the Palaeozoic: A role of eclogitization within the uppermost mantle

We examine the Tunguska Basin evolution by using two lithologic-stratigraphic sections along deep seismic sounding profiles and exploration wells. The tectonic analysis demonstrates that the subsidence of the basin was rapid in the Early Cambrian and slower since the Middle Cambrian. We show that the relative thinning of the crust beneath the basin is several times greater than its relative stretching, and therefore the stretching alone cannot explain the subsidence of the Tunguska Basin. We suggest a possible mechanism of the basin formation in the Palaeozoic. The thinning of the lithosphere beneath the Tunguska Basin due to ocean basin opening in its vicinity leads to passive uplift of the asthenosphere and to partial melting of mantle materials. The forming mechanism includes accumulation of magmatic melt in the asthenospheric bulge, phase transition to eclogite, and a flow in the upper mantle induced by the evolved heavy bodies. We construct a numerical model of basin evolution, compute the viscous flow due to the subsidence of an eclogite body, and find the resultant changes in the surface topography. To do this, we employ the Galerkin-spline technique. Using results of the model and tectonic analysis, we interpret geodynamic evolution of the Tunguska Basin and discuss the effect of phase changes in the upper mantle upon the evolution of the basin. The numerical results show that the subsidence curve calculated from the model gives a better fit to the observed tectonic subsidence than the thermal subsidence curves predicted by McKenzie's stretching model. The density distribution accepted in the model agrees with the upper-mantle velocity structure beneath the Tunguska Basin. The model is also consistent with gravity and heat flow data.

In-Situ X-Ray Characterization of LiMn2O4: A Comparison of Structural and Electrochemical Behavior

ABSTRACTLixMn2O4 materials are of considerable interest in battery research and development. The crystal structure of this material can significantly affect the electrochemical performance. The ability to monitor the changes of the crystal structure during use, that is during electrochemical cycling, would prove useful to verify these types of structural changes. We report in-situ XRD measurements of LiMn2O4 cathodes with the use of an electrochemical cell designed for in-situ X-ray analysis. Cells prepared using this cell design allow investigation of the changes in the LiMn2O4 structure during charge and discharge. We describe the variation in lattice parameters along the voltage plateaus and consider the structural changes in terms of the electrochemical results on each cell. Kinetic effects of LiMn2O4 phase changes are also addressed. Applications of the in-situ cell to other compounds such as LiCoO2 cathodes and carbon anodes are presented as well.

The influence of phase changes on debris-cloud interactions with protected structures

The physical state of the debris cloud generated by the interaction of a projectile with a thin target depends on the energy balance associated with the impact event. At impact velocities well above the sound speeds of the materials involved, the cloud is expected to consist of material in solid, liquid, and vapor phases. A series of numerical calculations using the multi-dimensional finite-difference hydrocode CTH has been used to evaluate the effect of phase changes ( i.e., different vapor fractions) on these clouds, and on their subsequent interaction with backwall structures. In the calculations, higher concentrations of vapor are achieved either by (1) increasing the initial temperature of both the projectile and the thin shield while keeping the impact velocity constant, or (2) by actually increasing the impact velocity. The nature of the debris cloud and its subsequent loading on the protected structure depend on both its thermal and physical state. This interaction can cause rupture, spallation, or simply bulging of the backwall. These computational results are discussed and compared with new experimental observations obtained at an impact velocity of ∼ 10 km/s. In the experiment, the debris cloud was generated by the impact of a plate-shaped titanium projectile with a thin titanium shield.

The effect of phase changes on target response

This paper presents the results of two impact studies with lead projectiles and lead targets. Impact velocity varied between 2.65 and 8.3 km/s, a range of velocities that induces a range of response in lead from fragmentation to vaporization. The first study considers the response of a lead target to impact by a 1.5 mm tungsten carbide sphere. Target response measurements included crater parameters and target momentum. Normalized target momentum, i.e. the ratio of target to projectile momentum, was observed to increase non-linearly with impact velocity, obtaining a value of 7.1 at 8.3 km/s. The second study compares the response of a shielded aluminum target to impact by either a lead or molybdenum projectile (the shield material was the same as the projectile). Test variables included shield to target spacing, shield thickness, target orientation and impact velocity. The four test variables affected the two test conditions differently, with the most similar results observed for tests with thick shields, minimal spacing and low impact velocity.

Catastrophic overturn of the Earth's mantle driven by multiple phase changes and internal heat generation

The effects of phase changes and strong internal heat generation may combine to bring about brief, but extremely intense episodes of rapid thermal convection in the Earth's mantle. Numerical calculations using realistic thermodynamic properties for the exothermic Olivine → Spinel and endothermic Spinel → Perovskite + Magnesiowustite phase transitions suggest the transition region of the Earth's mantle may act as a capacitor for subducting slabs. Slab material accumulates in the transition region until a threshold level of thermal buoyancy is reached, and is then rapidly discharged into the lower mantle. In my calculations, this occurs as a catastrophic burst of convection lasting ∼10 Myr, with elevated heat transfer rates lasting ∼100 Myr. Such episodes may be analogs to superplume activity which has been hypothesized to give rise to an intense episode of intra‐plate volcanism and stabilize the geodynamo against reversals. The topography on the two phase change boundaries is found to be negatively correlated, with the correlation becoming more negative during periods of rapid convection. Furthermore, the results of this study suggest the transition region of the Earth's mantle could be ∼250 K cooler on average, and consequently more viscous, than the surrounding mantle.

On the behaviour of baroclinic waves undergoing horizontal deformation. II: Error‐bound amplification and Rossby wave diagnostics

AbstractAn expression for the maximum possible amplification of a baroclinic wave with zero potential vorticity, undergoing horizontal deformation, is obtained. This amplification provides an estimate of the growth of hypothetical analysis errors for such a system. For the geophysically relevant flows considered in detail in this paper, strain rates of ±1 × 10−5 s−1 cause a 28% reduction in the logarithmic amplification over a 48‐hour period. If the effects of phase changes of water are simulated by halving the brunt‐Väisälä frequency, all growth rates are larger, but strain rated of ±1 × 10−5s−1 now cause a 34% reduction logarithmic amplification. Notably, this corresponds to an 81% reduction in actual amplification. For all strain rates the increase in non‐modal growth associated with lowering the Richardson number is found to be less than for norma‐mode‐type baroclinic waves.To understand why particular initial zonal wavelengths and vertical phase shifts optimize growth in this time‐dependent basic state, new diagnostics are developed. The diagnostics are based on a mathematical model of Bretherton's qualitative description of baroclinic instability in terms of two counter‐propagating Rossby waves. They provide a viewpoint from which growth results form the product of a scale term, which is proportional to the wind strength induced at opposing boundaries, and a phase term, which is maximized when the upper wave is 90° up shear of the lower Rossby wave. The perspective leads to a simple explanation of why strain affects amplification and how this effect depends on the static stability. Furthermore, it provides simple methods, based on diagnosed amplitudes of neglected 2nd and 3rd order nonlinear terms, for forecasting when linear prediction become misleading.To assess how dynamic constraints associated with the time dependence of a basis flow affect its stability, it proves useful to define a new quantity, the ‘potential maximal wave amplification’, which is the amplification that would arise if at each instant the flow was adiabatically and mass preservingly rearranged so that the Rossby waves defining the boundary buoyancy distribution were always optimally configured for growth.The results presented here also show that time‐dependent systems which do not support normal modes can amplify certain wavelengths more than other, and hence be likely to impart the corresponding horizontal structures onto arbitrarily shaped initial disturbances. Such scale selection is linked to the relationship between the horizontal morphology of a Rossby wave and the strength of the wind it can induce at vertically distant points.The effect of strain on sets of flows is also found to depend on the mean meridional wave number of such flows. Notably, if this mean meridional wave number is increased to values near the short‐wave cut‐off for instability, the presence of strain can actually enhance growth.In narrow baroclinic jets, such as those found off ice edges in polar regions, barotropic modes often grow faster than baroclinic modes in unstrained flow. A comparison with the effects of strain on barotropic instability shows that frontogenetic strain damps barotropic growth much more than baroclinic growth. The result may be important to theories of polar‐low genesis.

Effects of Phase Changes in Low-numbered Harmonics on the Internal Representation of Complex Sounds

A series of experiments investigated the effect of phase changes in low-numbered single harmonics in target sounds that were either synthesized steady-state vowels fo periodic signals having only a single formant. A matching procedure was sued in which subjects selected a sound along a continuum differing in first formant frequency in order to get the best match with the target sound; perceptual effects of the phase manipulations in the target were detected as a change in the matched first formant frequency. Stimuli had to contain at least three harmonics to produce the effect, but id did not require a particular starting phase of the components. A suppression phenomenon is discussed, in which phase changes alter the phase-locking characteristics of auditory fibres tuned to low-numbered harmonics.

Recent developments in the lusas finite element system

This paper focuses on some of the recent developments implemented in the LUSAS finite element system. These developments include: a composite/laminated shell model formulated using a general multilayer semiloof shell element that permits arbitrary composite layups of isotropic, orthotropic, elastoplastic and concrete materials, backward Euler stress return algorithms for efficient elastoplastic analysis using von Mises criterion, slideline procedures for modelling impact and large relative deformation between two or more surfaces of a structure, nonlinear thermal capabilities including the effects of phase changes and nonlinear radiative heat transfer, and a fully coupled thermo-mechanical functionality.

The Effect of Possible Phase Changes on the Heat Conduction of Slags

The Effect of Possible Phase Changes on the Heat Conduction of Slags

The effect of volume phase changes, mass transport, sunlight penetration, and densification on the thermal regime of icy regoliths

A thermal model is presented which quantitatively accounts for the effects of sublimation condensation, and convection throughout a volume of a porous ice crust subjected to solar insolation. The effect of penetration of insolation into ice that is translucent to visible radiation but opaque to infrared radiation is also included. The governing energy differential equation, which also satisfies conservation of mass and accounts for the possibility of free molecular or continuum flow, is solved for various conditions defined by a reasonable range of thermal conductivities, sunlight absorption coefficients, and pore sizes. Quasi-steady-state temperatures, H 2O mass fluxes, and rates of change of mass density for the ice are computed as functions of depth and time of day. We find that, when the effects of latent heat and mass transport are included in the model, the increase in the near surface temperature (the boundary condition for crustal heat flow) brought about by the “solid-state greenhouse” is greatly diminished. If the lowest thermal conductivities reported for the surface of Europa (∼100 erg/cm sec K) are assumed to apply to the upper crust as well, the melting point could be approached at very shallow depth. However, this is precluded except as a transient and shallow phenomenon which could not affect deep crustal temperatures because densification would raise the thermal conductivity to ≥1000 erg cm −1 sec −1 K in the underlying material in a geologically negligible period of time. If thermal conductivities ≥1000 erg/cm sec K are assumed, then the greenhouse effect raises near-surface temperatures ≤35 K, but the densification is slow enough that deep crustal temperatures would be augmented, allowing for melting at a depth of 7–19 km, depending on assumptions concerning tidal dissipation. Thus, when the effects of latent heat, mass transport, and densification are all taken into account, the existence of a significant solid-state greenhouse effect can be shown to be compatible both with morphological evidence for significant crustal strength and with evidence for decoupling of the icy shell from the lithosphere.

Effects of phase changes in low‐numbered harmonics on formant frequency matches

Phase changes to single harmonics (of a 125‐Hz fundamental) in the first formant (F1) region can change the phoneme boundary between /I/ and /e/ along an F1 continuum in an identification task [C. J. Darwin and R. B. Gardner, J. Acoust. Soc. Am. 79, 838–845 (1986)]. Physiological correlates of this effect have been noted in the ALSR response of guinea‐pig auditory nerve fibers [A. R. Palmer et al., in The Psychophysics of Speech Perception, edited by M. E. H. Schouten (Nijhoff, Dordrecht, 1987)] and in an auditory model with synchrony suppression. The present work demonstrates similar phase effects using a matching paradigm. Subjects matched sounds along a continuum that differed in F1 frequency and could have additional formants. The target sounds (fundamental = 125 Hz; F1 = 440 Hz) were taken from the matching continuum but had the phase of a single harmonic changed. Systematic and consistent differences in the matched F1 value were found as a function of phase. Although the starting phase of the components influenced the size of the matched difference in F1, the difference was still present for randomized starting phases. The effect required at least three frequency components and varied with fundamental frequency.

Common reference coherence data are confounded by power and phase effects

Coherence analysis of the EEG is used to study the coupling between cortical regions. High coherence between signals recorded at 2 electrodes is interpreted as evidence for neuroanatomic connections between the cortical areas underlying the electrodes. When common reference recordings are used, coherence measures the relationship between 2 time series, each of which is the difference between 2 signals measured at the scalp and is confounded by spectral power and phase at the recording and reference electrodes. Using multi-channel EEG data from 3 subjects, we illustrate the confounding of common reference data coherence computations and demonstrate the extreme effects of power and phase changes on coherence by simulating these changes in the EEG data. Common reference coherence data can be either inflated or deflated as a consequence of activity (i.e., spectral power) at the reference. Phase relationships among the reference and recording time series modulate the power effects on coherence. Both the power and phase effects can vary dramatically across frequencies, having profound and complicated effects on the shape of the coherence function. Based on these considerations, we conclude that common reference coherence data must be interpreted very cautiously and recommend that a new body of EEG coherence data must be gathered using reference-free recording methods before the utility of EEG coherence analysis for understanding brain function can be determined.

Experimental approaches to the study of deformation/metamorphism relationships

AbstractRock deformation and metamorphism can interact at the mechanistic level in the following ways: (a) facilitation of cataclasis through the release of high-pressure fluid during dehydration and decarbonation reactions; (b) facilitation of intracrystalline plasticity through the stresses induced during solid-state volume changes; (c) enhanced deformability through the transient existence of fine-grained reaction products; (d) modification of chemical potential gradients driving diffusion if a reaction can occur along the diffusion path; (f) changes in the resistance to intracrystalline plasticity through the effect of reaction-induced changes, pore fluid pressure and chemistry on point defect chemistry of the solid phases.Examples of experimental studies of each of these types of interaction are described. Special experimental problems arise through: (i) the effects of solid phase and pore space volume changes, and their effects on pore fluid pressure and measured strain; (ii) the effects of such microstructural changes on the determination of flow law parameters; and (iii) in many instances the need for very long duration deformation experiments if reaction kinetics are sluggish.There is an outstanding need for experimental studies of the effects of non-hydrostatic stress on the conditions for the onset of metamorphic reactions and phase transformations, as a basis for understanding some classes of deformation/metamorphism interaction. However, it is emphasized that the threefold classification of rock deformation mechanisms into cataclastic, crystal-plastic, and diffusive mass transfer processes, established from the study of deformation of monomineralic rocks, forms an essential framework for the understanding of deformation/metamorphism inter-relationships.

The Poley absorption in liquid crystals

The far infrared torsional oscillatory absorption of a nematic liquid crystal has been isolated for the first time free of higher frequency proper modes. This has been achieved using a molecule specially synthesised for this purpose with a dipole moment engineered perpendicular to the long axis so that torsional oscillation about this axis modulates this component only. The far infra-red power absorption of the liquid crystal in the isotropic, nematic, solid and supercooled conditions is therefore a Poley absorption, i.e. the torsional oscillation about the rigid long axis of the liquid crystal molecule itself. The effect of phase changes on a macroscopic level is to sharpen and intensify this absorption. This is clear evidence to the effect that phase changes in liquid crystals are cooperative phenomena, the molecular librational dynamics about the long axis are little different from those in a regular molecular liquid.

Phase transitions and convection in Icy satellites

The effects of solid‐solid phase changes on subsolidus convection in the large icy moons of the outer solar system are considered. Phase transitions affect convection via processes that distort the phase change boundary and/or influence buoyancy through thermal expansion. Linear stability analyses are carried out for ice layers with a phase change at the midplane. Two exothermic phase transitions (ice I ‐ ice II, ice VI ‐ ice VIII) and two endothermic transitions (ice I ‐ ice III, ice II ‐ ice V) are considered. For the exothermic cases, the phase change can either impede or enhance whole‐layer convection. For the endothermic cases, the phase change always inhibits whole‐layer convective overturn and tends to enforce two‐layer convection. These results place some constraints on possible models of icy satellite evolution and structure.