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Rodents are characterised by a distinctive masticatory apparatus which includes a single pair of enlarged and continually growing incisors. This morphology, termed diprotodonty, has also independently evolved in a number of other mammals, including the aye-aye. This study examined the functional significance of the internal “root” of the elongated rodent-like incisor. The mandibles of four rodents and an aye-aye were modelled to exhibit incrementally shorter incisor roots. Finite element analysis was used to predict stress and strain patterns across the jaw to determine whether the length of the incisor root contributes to the resistance of mechanical forces encountered in the mandible during incision. It was found that von Mises stresses increase in the region of the mandible local to where the incisor is removed, but that the stress distribution across the wider mandible is only minimally affected. Thus, the long internal incisor appears to play a small role in resisting bending forces close to the incisor alveolus, and may act with the arch-like mandibular shape to strengthen the mandible in this region. However, the impact across the whole mandible is relatively limited, suggesting the highly elongate incisor in diprotodont mammals may be principally driven by other factors such as rapid incisor wear.

Rodents are characterised by a distinctive masticatory apparatus which includes a single pair of enlarged and continually growing incisors. This morphology, termed diprotodonty, has also independently evolved in a number of other mammals, including the aye-aye. This study examined the functional significance of the internal "root" of the elongated rodent-like incisor. The mandibles of four rodents and an aye-aye were modelled to exhibit incrementally shorter incisor roots. Finite element analysis was used to predict stress and strain patterns across the jaw to determine whether the length of the incisor root contributes to the resistance of mechanical forces encountered in the mandible during incision. It was found that von Mises stresses increase in the region of the mandible local to where the incisor is removed, but that the stress distribution across the wider mandible is only minimally affected. Thus, the long internal incisor appears to play a small role in resisting bending forces close to the incisor alveolus, and may act with the arch-like mandibular shape to strengthen the mandible in this region. However, the impact across the whole mandible is relatively limited, suggesting the highly elongate incisor in diprotodont mammals may be principally driven by other factors such as rapid incisor wear.

An approach for obtaining a Schrodinger equation for a spinless nonrelativistic particle with a position-dependent mass is proposed. Rather than starting with the nonrelativistic hamiltonian for a free particle, we begin with its relativistic completion in the form of a Klein–Gordon equation and then reduce it to obtain the nonrelativistic limit. This type of procedure avoids the usual ordering ambiguities that commonly arise in obtaining a Schrodinger equation for a particle with position-dependent mass.

All rodents possess a single pair of enlarged incisors that grow throughout life. This condition (diprotodonty) is characteristic of Rodentia, but is also found in other mammals such as lagomorphs, hyraxes, the aye-aye and common wombat. This study surveyed lower incisor morphology across extant diprotodonts to examine shape variation within and between rodents and other diprotodonts, and to determine if tooth shape varies in a manner predictable from mechanics. Six linear and area variables were recorded from microCT scans of the mandibles of 33 diprotodont mammals. The curvature of the rodent lower incisors, as measured by the proportion of a circle it occupies, was shown to vary between 20 and 45%, with non-Glires taxa falling outside this range. Relative lengths of the portions of the incisor within and external to the mandible were not significantly correlated when the overall size was taken into account. Cross-sectional geometry of the incisor was significantly correlated with the external length of the incisor. Overall, incisor morphology was shown to vary in a way predictable from ecology and mechanics, in order to resist bending. Among non-rodents, lagomorph incisors closely resemble those of rodents, and, relative to rodents, hyrax and wombat incisors are somewhat smaller but aye-aye incisors are much more extreme in morphology.

All rodents possess a single pair of enlarged incisors that grow throughout life. This condition (diprotodonty) is characteristic of Rodentia, but is also found in other mammals such as lagomorphs, hyraxes, the aye-aye and common wombat. This study surveyed lower incisor morphology across extant diprotodonts to examine shape variation within and between rodents and other diprotodonts, and to determine if tooth shape varies in a manner predictable from mechanics. Six linear and area variables were recorded from microCT scans of the mandibles of 33 diprotodont mammals. The curvature of the rodent lower incisors, as measured by the proportion of a circle it occupies, was shown to vary between 20 and 45%, with non-Glires taxa falling outside this range. Relative lengths of the portions of the incisor within and external to the mandible were not significantly correlated when the overall size was taken into account. Cross-sectional geometry of the incisor was significantly correlated with the external length of the incisor. Overall, incisor morphology was shown to vary in a way predictable from ecology and mechanics, in order to resist bending. Among non-rodents, lagomorph incisors closely resemble those of rodents, and, relative to rodents, hyrax and wombat incisors are somewhat smaller but aye-aye incisors are much more extreme in morphology.

We consider the possibility of the detection of a chameleon effect by an earth orbiting satellite such as LAGEOS, and possible constraints that might be placed on chameleon model parameters. Approximate constraints presented here result from using a simple monopole approximation for the gravitational field of the earth, along with results from the Khoury-Weltman chameleon model, solar system constraints obtained from the Cassini mission, and parameter bounds obtained from the LAGEOS satellite. It is furthermore suggested that a comparison of ground-based and space-based multipole moments of the geopotential could reveal a possible chameleon effect., Comment: 13 pages; to appear in Astrophys.Space Sci

We consider here the interaction of scalar bosons with a topological domain wall. Not only is there a continuum of scattering states, but there is also an interesting "quasi-discretuum" of positive energy bosonic bound states, describing bosons entrapped within the wall's core. The full spectrum of the scattering and bound state energies and eigenstates is obtainable from a Schr\"odinger-type of equation with a P\"oschl-Teller potential. We also consider the presence of a boson gas within the wall and high energy boson emission., Comment: 5 pages; To appear in Quantum Stud: Math. Found

This paper discusses approaches to improve the accuracy of onshore pipeline remaining life assessments and optimise the targeting of locations for field verification activities via detailed assessment of reported corrosion metal losses and corrosion feature interactions. The overall aim is to show how confidence in assessments can be increased while ensuring adherence to industry standards. Evaluation of interactions between corrosion features is a necessary consideration as specified in industry standard fitness-for-service (FFS) methodologies. In accordance with developed FFS standards, if corrosion features are sufficiently close together, they should be considered to act as a single, larger feature. However, in the authors' experience, detailed assessment of corrosion feature interactions is not always performed. This can lead to overly optimistic/pessimistic results, and a subsequent lack of focus for future field verification activities with respect to inspection locations and techniques. FFS assessments are often based on results from in-line inspections (ILIs), which, depending on the pipeline condition, can report many thousands of individual corrosion features. In the case of heavily corroded pipelines, where corrosion damage is reported along approximately the same orientation (for example at 06:00, the bottom of the line), inadequate consideration of corrosion feature interactions could significantly overestimate the maximum allowable safe pressure of the pipeline. In contrast, conservatively assuming a grooving metal loss morphology and simplifying FFS calculations to assume infinitely long corrosion can appreciably lower calculated safe pressures, resulting in premature remediation activities (such as repairs, de-rating). In both cases, neither method of assessment allows specific targeting of field verification activities as areas of maximum corrosion interaction will not have been determined. This paper will demonstrate the benefits of performing a detailed assessment of corrosion feature interactions during an integrity assessment in comparison to overly optimistic or simplified assumptions, and show the benefits of such detailed assessment with respect to future field verification activities.

An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A substantial generalization of a previously studied nonlinear oscillator with variable mass is obtained, wherein the position dependence of the mass of a nonrelativistic particle is due to a dilatonic coupling function emerging from the extra dimension. Previously obtained solutions for such systems can be extended and reinterpreted as nonrelativistic particles interacting with dilaton fields, which, themselves, can have interesting structures. An application is presented for the nonlinear oscillator, where within the new scenario the particle is coupled to a dilatonic string., Comment: 11 pages, no figs; To appear in Quantum Stud: Math. Found

The dynamics of dissociation and negative ion formation have been investigated for the hyperthermal energy scattering of state-selected OCS+(X 2Πx, υ1, υ2, υ3) on Ag(111). Experiments reveal the effect that collision energy and internal energy have on the formation of scattered ionic products. An analysis of the appearance threshold and fragment velocity distribution for each scattered product channel [S−(2P), O−(2P), and SO−(X 2Π)] suggests that three distinct fragmentation mechanisms compete. Prompt impulsive dissociation of neutralized OCS+(X 2Π), followed by electron attachment to the nascent O fragment, is responsible for O−(2P) emergence. The production of SO−(X 2Π) relies on a collisionally activated distortion of OCS, forcing the O and S atoms close together while ejecting the central carbon atom. Finally, a comparison between the scattering of state-selected OCS+(X 2Πx, υ1, υ2, υ3) and S+(4S) on Ag(111) provides strong evidence that dissociative neutralization of OCS+(X 2Πx, υ1, υ2, υ3) leads to ...

The processes of electron transfer and dissociative scattering are explored for collisions of state-selected hyperthermal energy (5–80 eV) NO+(X1Σ+, ν) on GaAs(110) and Ag(111). In conjunction with classical and quantum mechanical calculations, the experimental data reveal the sequence of neutralization, dissociation, and electron attachment steps responsible for the emergence of O−(2P) ions. This mechanism is compared to those which govern the formation of negative ion fragments in the scattering of state-selected OCS + (X 2 II 3 2 ) on Ag(111). In the scattering of OCS+, impulsive mechanical dissociation forms O−(2P) ions; dissociative neutralization leads to S−(2P); and atom elimination yields SO−(2II).

Recently reported molecular ion/surface scattering experiments suggest that translational and vibrational energies each have a distinct influence on molecular dissociation for the NO+/GaAs(110) system [J. Chem. Phys. 1994, 100, 6791]. To interrogate the coupling between vibrational and translational degrees of freedom, classical trajectory simulations were performed. The dissociation dynamics and energy transfer processes were examined for three different molecule/surface repulsive potentials: a Born−Mayer potential, a Ziegler−Biersack−Littmark potential, and a Hartree−Fock potential. In each case, the calculated product appearance thresholds and average product translational energies are qualitatively consistent with the aforementioned experimental results. In all, this suggests that translational energy activates dissociation via a collision-induced dissociation mechanism. Regarding initial molecular vibrational energy, the classical model shows that the relative dissociation probability depends on vib...

The processes of electron transfer and dissociative scattering are explored for collisions of hyperthermal NO + on GaAs(110). The experiments reveal a marked angular dependence to O − emergence. A strong correlation between the O − scattering angle and the final atom-surface interaction site provides a map of the lateral dependence to reactivity. The results are modeled by sequential neutralization, dissociation, and electron attachment steps. Classical trajectory calculations, in conjunction with an empirical opacity function, accurately reproduce the experimental results. The opacity function is interpreted as the probability that an electron will attach to a departing O fragment as a function of the last surface site the atom impacts. The experiments indicate that O − emergence occurs predominantly for oxygen atoms which come in close contact with the localized dangling bond states of GaAs(110).

Hyperthermal energy reactions of NO+ with Ag(111) were studied as a function of collision energy and the incident diatom’s internuclear‐axis direction. Laser photoselection via (1+1’) resonance enhanced multiphoton ionization (REMPI) prepared an aligned distribution of NO+(X 1Σ+, Etrans, v=0, J) prior to the molecules impact with the surface. The emergence of scattered O− products was enhanced when NO+ approached the surface with an ‘‘end‐on’’ rather than a ‘‘side‐on’’ orientation. Moreover, the magnitude of the reaction’s alignment preference increased with decreasing collision energy. The appearance threshold for O− was approximately 20 eV. Classical trajectory calculations demonstrated that these results are consistent with a collision‐induced dissociation mechanism mediated by both vibrational and rotational excitation upon impact. Reorientation of the internuclear axis during the collision drastically affects the simulated dissociation dynamics. No alignment preference for scattered NO− emergence cou...

The reactivity of a molecule striking a surface was found to depend on the diatom's internuclear-axis alignment. State-selected NO+ (X1Σ+, v = 0, J) reagents were aligned through laser ionization prior to their impact with a Ag(111) surface. The yield of scattered O− products was enhanced by “end-on” type collisions, and this preference diminished as the collision energy increased from 35 to 80 eV. Classical trajectory calculations showed that a collision-induced dissociation model is consistent with the experimental observations.

The scattering of state‐selected NO+(X 1Σ+, v=0–6) on GaAs(110) was explored across the hyperthermal energy region. Relative yields and velocity distributions for scattered anionic products NO−(X 3Σ−, v=0) and O−(2P) were measured as a function of the number of vibrational quanta and collision energy for NO+(X 1Σ+, v=0–6) incident on the surface. Facile neutralization along the inbound trajectory forms vibrationally excited NO(2Π) immediately prior to surface impact. Electron attachment to form NO−(X 3Σ−, v=0) occurs near the distance of closest approach between the molecule and surface. With regard to O−(2P) emergence, a collision‐induced dissociation mechanism is consistent with the observed 25 eV threshold. Incident vibrational energy is as much as ten times more effective than translational energy in forming O−(2P). This paper represents the first experimental investigation into the effect of vibrational energy on electron transfer and dissociation of ions at surfaces and highlights the unique interpl...

A group housing system for sows, the Hurnik-Morris (HM) system, was developed to address several of the perceived animal welfare limitations of existing housing methods. The HM system permits socially coordinated eating and resting, controlled and socially undisturbed feed intake, physical exercise, and regular exposure to boars. The HM system effectively uses and reinforces the behavioral phenomenon of the social synchronization of feeding and provides a less restrictive housing environment. The system provides housing for sows in small groups and an individual, non-competitive feeding environment using electronic feeding compartments. Gilts reared during gestation in the HM system were observed to spend less time lying in sternal recumbency (31 vs 21%; P = .004) and performing stereotypies (.10 vs .56%; P = .034) and to spend more time participating in social activities (1.4 vs .19%; P = .0007) than similar gilts kept in gestation crates (GC). The HM sows revealed a significantly longer latent period to postprandial lying than did GC gilts (64 vs 32 min; P = .0001). The order of gilt entry into the feeding compartments tended to be more consistent than the sequence of feeding compartments being entered (W = .57 vs .41; P = .06). This indicates that social factors seemed to be more important than spatial ones in determining the order of entry into the feeder compartments.

A hyperthermal beam of state‐selected NO+ X Σ+(v=0–6) ions is scattered on a clean, well‐characterized GaAs(110) surface. The threshold for the appearance of scattered O− ions occurs at a collision energy of 25 eV. Vibrational energy proves to be an order of magnitude more effective than translational energy in enhancing the yield in this channel.

The effect of a new group housing system on performance (132 gilts and litters) and endocrinological (35 gilts) and immunological functions (28 gilts) was studied. Animals were randomly assigned to a conventional system (control), involving greater than 2 mo in individual stalls, or to the Hurnik-Morris (H-M) housing system, involving continuous housing in small groups, for breeding-gestating swine. The gilts were reared throughout gestation in their respective housing systems and moved 3 to 5 d prefarrowing to a common farrowing facility. Various production data were collected, including sow weight and backfat measurements, number of pigs born, number born alive, number weaned, litter birth weight, and litter weaning weight. An adrenal function test using dexamethasone pretreatment and ACTH1-24 challenge was imposed on gilts 5 d prebreeding and once between d 81 to 87 of gestation. Plasma progesterone was measured at the same time. Immune function was measured by serum antibody response to hen egg white lysozyme (HEWL) and delayed-type hypersensitivity (DTH) to tuberculin. Gilts reared in the H-M housing system exhibited a number of pigs weaned per litter and litter weaning weights comparable to the number and weights in the control system (7.3 +/- .33 vs 6.9 +/- .38, P = .421 and 56.9 +/- 2.42 kg vs 51.3 +/- 2.76 kg, P = .132, respectively). Prefarrowing and weaning backfat measurements were significantly reduced in group-housed gilts (15.8 +/- .45 mm vs 17.8 +/- .55 mm, P = .005 and 14.6 +/- .4 mm vs 16.2 +/- .42 mm, P = .008, respectively).(ABSTRACT TRUNCATED AT 250 WORDS)

We present a study of finite-size effects in a model exhibiting a first-order temperature-driven symmetry-breaking structural phase transition in theL⊥×∞ cylindrical geometry in theL⊥→∞ limit. Exact studies demonstrate the applicability of our scaling ansatz even in the one-dimensional limit, making this model ideal for studying finite-size effects. The scaling ansatz, similar to the previously developed ansatz for field-driven transitions, demonstrates that latent heat is crucial in driving these transitions. This ansatz is supported by a 2×2 phenomenological transfer matrix based upon the symmetries of the system; this produces an analytic free energy which has the scaling form. Order parameter probability distributions show that the high- and low-temperature phases coexist only in a small finite-size-affected regime near the bulk transition temperature; this regime vanishes exponentially fast asL⊥ diverges.

The effect of administration of porcine somatotropin (pST) on the production efficiency and economic returns of market hog production was determined based on temperate climate production and carcass merit marketing systems. No differences were detected in average daily gain (ADG), feed efficiency (FE) or carcass index for pigs receiving the same total dose (50 μg kg−1 d−1) of pST from 5 to 15 wk of age (9–50 kg) in any of three administration patterns (pST once per day, n = 12; pST once per day for 7 d and no injection for the next 7 d repeated, n = 11; pST once every 3 d, n = 11). However, when pST was administered from 15 wk of age through market weight (50–96 kg, n = 18), ADG increased 15.4% (P −1) and feed costs (S160.00–$240.00 CDN t−1). These results indicate that application of pST to pigs in the finisher phase of growth would result in improved production efficiency and significant economic return under present hog marketing conditions in Canada where carcass merit settlement is used without an increase in carcass weight. Key words: Porcine, somatotropin, growth, economic returns, production

We have studied a Hamiltonian that models the change in effective interactions leading to a change in phonon dispersion relations that occurs at a diffusionless first-order structural phase transition. This change produces lower frequency phonons and correspondingly a higher vibrational entropy in the high-temperature phase, relative to the low-temperature phase. Mean-field and self-consistent phonon theories predict that this entropy stabilizes the high-temperature phase with respect to the low-temperature phase, producing a more strongly first-order transition and a lower transition temperature. Close agreement between exact calculations and self-consistent phonon theory indicates that the system is essentially harmonic, except in a very small temperature region near the transition. In this region exact calculations show the presence of large-amplitude fluctuations connecting the high- and low-temperature phases. Molecular-dynamic simulations of the system suggest that these heterophase fluctuations show diffusive behavior, and are associated with a central peak in the dynamical structure factor.

SynopsisThe purpose of this paper is to introduce a fibrewise generalisation of category, in the sense of Lusternik–Schnirelmann. This reduces to the classical concept when the space is a point. Fibrewise category may be compared with equivariant category, which has been the subject of some recent research [1,7,8]. Many variations on the basic idea of category have been discussed in the literature, for example the concept of category of a map, but since the generalisations to the fibrewise case are fairly routine they are not considered here.

We propose a new temperature-independent Hamiltonian that displays a vibrational-entropy-driven, first-order phase transition. Models of this kind do not presently exist in the statistical-mechanics literature, but are important in providing a simple realization of diffusionless, solid-to-solid martensitic transitions. The model employs anharmonic couplings between neighboring particles that cause the low-temperature phase to have a lower vibrational entropy (i.e., stiffer restoring forces) than the high-temperature phase. This entropy difference, as opposed to an internal energy difference, produces a sharp transition. In one dimension the model may be solved exactly using transfer-integral techniques, and the solutions show heterophase fluctuations connecting the parent and product phases only for temperatures very close to the transition. Consistent with this behavior, {ital S}({ital q},{omega}) found from molecular-dynamics simulations shows a central peak that is diffusive in origin.

A group housing system for sows, the Hurnik-Morris (H-M) System, is described which addresses several of the serious animal welfare limitations of existing housing methods. The H-M System permits socially coordinated eating and resting, controlled and socially undisturbed feed consumption, physical exercise and regular exposure to boars. Sows adjusted relatively rapidly to the H-M System, indicating that its design concurs with their perceptual and learning capabilities. Key words: Swine, housing, behavior, welfare

We describe modeling and simulation of long-range terrestrial laser communications links between static and mobile platforms. Atmospheric turbulence modeling, along with pointing, tracking and acquisition models are combined to provide an overall capability to estimate communications link performance.

We introduce a wave-optics based simulation code written to model a complete free space laser communications link, including a detailed model of an adaptive optics compensation system. We present the results obtained by this model, where the phase of a communications laser beam is corrected, after it propagates through a turbulent atmosphere. The phase of the received laser beam is measured using a Shack-Hartmann wavefront sensor, and the correction method utilizes a MEMS mirror. Strehl improvement and amount of power coupled to the receiving fiber results for both 1 km horizontal and 28 km slant paths will be presented.

Specific antibodies against the C-terminus of E2, produced by affinity purification of polyclonal antisera, have been used to identify the cellular populations which express the HPV 16 E2 transcription factor, in a series of formalin-fixed, paraffin-embedded cervical tissues. Cases were selected for both the presence of HPV 16 DNA (confirmed by multiple gene-specific PCR detections) and the presence of multiple grades of cervical intraepithelial neoplasia (CIN). The data indicate that E2 expression is highest in CIN I and in koilocytic lesions. Lower expression was observed in CIN II and little in CIN III lesions. In contrast, there was some restoration of E2 expression in invasive carcinomas, although the intracellular distribution was much more diffuse. The location of E2 expression to the superficial layers of the cervical epithelium, as well as the occurrence of some basal expression in CIN I, suggests that antibodies against HPV 16 E2 could be a useful adjunct to standard histological techniques for the detection of 'at-risk' patients as part of a cervical screening programme.

Sows were randomly selected and assigned to either the Hurnik-Morris system (HM; n = 59) or a conventional gestation crate system (GC; n = 90) before breeding. The HM system provides housing for sows in small groups. All sows were bred to Duroc x Hampshire commercial boars. A common farrowing barn with 18 farrowing crates was used for the HM and GC sows. The HM sows had less (P

LLNL has utilized optical parametric oscillator technology to develop and field a rapidly-tunable mid-wave IR DIAL system. The system can be tuned at up to 1 KHz over the 3.3- 3.8 micron spectral region, where hydrogen-bond stretching modes provide spectroscopic signatures for a wide variety of chemicals. We have fielded the DIAL system on the LLNL site on range, turbulence, and receiver aperture size. In this paper we describe the interplay of turbulence and speckle to produce the observed nose fluctuations at short range.

Gilts (n = 187) were randomly assigned to either the Hurnik-Morris housing system (HM) or a conventional gestation crate system (GC) prior to breeding. The Hurnik-Morris system provides housing for sows in small groups. Gilts were synchronized for estrus and bred to Duroc Hampshire commercial crossbred boars. Gilts were reared in their respective housing systems through their gestation period. Housing system during breeding and gestation of sows did not affect their respective piglet mortality and piglet viability levels. The slightly higher feet and leg problem scores for the HM sows at weaning may indicate a necessity for farrowing accommodation that will allow movement of sows during lactation.

The purpose of the study was to estimate the anterior-posterior displacements that would occur with total knee prosthetic designs of different sagittal radii under functional conditions. A key question was whether some designs provided excessive constraint. Patients who had different total knee prosthetic designs were tested in a special rig where the AP drawer was measured under loaded and unloaded conditions. These same designs of total knee prostheses were then tested in a rig under different conditions of compressive and shear loads. Using these experiments as verification, a theoretical treatment was developed to predict the AP displacement for different activities. It was concluded that designs with low to moderate conformity required soft tissue restraint under more strenuous activities, or where high shear forces occurred under low compressive loads. Designs of moderate to high conformity could be fully self-stabilizing under all realistic conditions. However, for all designs, the AP displacement was only a few millimeters under functional loads, indicating that special care must be taken during surgery to avoid conflict between the condylar surfaces and the retained cruciate ligaments so that restriction of motion and excessive wear do not occur.

We have utilized resonance-enhanced multiphoton ionization in conjunction with ion optics to produce state-selected NO+(X1(Sigma) +, v equals 0 - 6, Etrans equals 8 - 80 eV) ions.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The architecture and major system components of the sodium-layer laser guide star system at LLNL will be described, and experimental results reported. The subsystems include the laser system, the beam delivery system including a pulse stretcher and beam pointing control, the beam director, and the telescope with its adaptive-optics package.

As a second-order phase transition is traversed critical scattering appears; these fluctuations serve notice of the impending loss of stability of the equilibrium phase. For a model first-order phase transition we [ital rigorously] prove, using [ital exact] thermodynamic quantities obtained from strip-transfer-matrix calculations, as well as finite-size-scaling analysis, that as a temperature-driven, symmetry-breaking, first-order phase transition is approached, no [ital enhancement] of fluctuations into the future product phase occurs. To be specific, we study the probability of occupation of the product phase (stable below the transition temperature), and demonstrate that this is a monotonically decreasing function as the transition temperature is approached from above. The relation of this pedagogical result to x-ray scattering experiments is discussed.