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At least 631 records · Page 35Linked to original sources

PubMed2000

Contrast-enhanced, three-dimensional power Doppler sonography for differentiation of adnexal masses.

OBJECTIVE: To investigate the potential usefulness of contrast-enhanced, three-dimensional power Doppler sonography in the differentiation of benign and malignant adnexal lesions. METHODS: A total of 45 patients with complex adnexal lesions of uncertain malignancy at transvaginal B mode and/or color Doppler sonography were prospectively evaluated with three-dimensional power Doppler sonography before and after injection of contrast agent. Presence of a penetrating pattern and a mixed penetrating and peripheral pattern suggested adnexal malignancy. All the results were compared with histopathology. RESULTS: There were 12 cases of ovarian malignancy and 33 benign adnexal lesions. Of the 12 ovarian cancers, seven (58. 3%) showed vascular distribution suggestive of malignancy at nonenhanced three-dimensional power Doppler sonography. After injection of contrast agent, a penetrating vascular pattern and/or a mixed penetrating and peripheral pattern were detected in all cases of ovarian malignancy. One cystadenofibroma demonstrated penetrating vessels at initial scan, whereas two benign lesions (fibroma and cystadenofibroma) were misdiagnosed as malignant at contrast-enhanced, three-dimensional power Doppler sonography. The use of a contrast agent with three-dimensional power Doppler sonography showed diagnostic efficiency (95.6%) that was superior to that of nonenhanced three-dimensional power Doppler sonography (86. 7%). CONCLUSION: Contrast-enhanced, three-dimensional power Doppler sonography provides better visualization of tumor vascularity in complex adnexal masses. If used together with three-dimensional morphologic ultrasound assessment, enhanced three-dimensional power Doppler imaging might precisely discriminate benign from malignant adnexal lesions.

Adult↗

PubMed2001

Assessment of myocardial perfusion by myocardial contrast echocardiography using harmonic power and the transvenous contrast agent SHU 563A in acute coronary occlusion and after reperfusion.

BACKGROUND: Harmonic power Doppler imaging is a novel technique for the assessment of myocardial perfusion by contrast echocardiography. In this study, we examined whether myocardial contrast echocardiography using harmonic power Doppler and the new transvenous contrast agent SHU 563A can identify myocardial perfusion defects during coronary occlusion and reperfusion. METHODS: To assess the potential of this technique, we occluded either the left anterior descending coronary artery or the circumflex coronary artery for 2 to 3 h followed by 1 h reperfusion in 10 dogs in an open chest model. After transvenous administration of SHU 563A, an air-filled, polymeric contrast agent, myocardial contrast echocardiography was performed in short and long axis views with triggered harmonic power Doppler imaging after coronary occlusion and reperfusion. Post-mortem triphenyl tetrazolium chloride staining was performed to verify infarction. Harmonic power Doppler and anatomic data were analyzed by independent observers. RESULTS: During coronary occlusion, harmonic power Doppler showed perfusion defects in all 10 dogs. The defect size in the short axis view at papillary muscle level ranged 4-51% (14+/-13%) and 3-43% (16+/-10%) in the long axis view (% total LV slice area). After reperfusion (1 h) and infusion of dipyridamole (0.56 mg/kg), power Doppler demonstrated perfusion defects in seven dogs: 0-20% (9+/-8%) (short axis view) and 0-48% (13+/-14%) (long axis view). Five dogs showed anatomic infarction. The anatomic infarct area was 0-18% (6+/-8%) (slices corresponding to the echocardiographic short axis images). Perfusion defect size by harmonic power Doppler correlated well with residual infarct size (r=0.82, P<0.01). CONCLUSIONS: Myocardial contrast echocardiography using harmonic power Doppler and the new contrast agent SHU 563A accurately displays perfusion defects during acute coronary occlusion and after reperfusion. The site and size of residual myocardial infarction is reliably identified on line, in color. This approach has excellent potential for clinical application.

Animals↗

PubMed2003

The power law can describe the 'entire' drug release curve from HPMC-based matrix tablets: a hypothesis.

The purposes of this study were to (i) re-examine the relevance of Higuchi equation and the power law using both simulated and experimental release data in conjunction with the linearized, in terms of t(1/2), percent of drug release plots, (ii) demonstrate that the power law describes the entire drug release profile of several experimental data, and (iii) point out a physically based hypothesis for the successful use of power law in describing the entire drug release profile. Simulated data generated from the equation of power law were further analyzed using linear regression analysis in accord with the Higuchi equation. The analysis revealed that data generated from the equation of power law can be misinterpreted as obeying the Higuchi equation. The use of power law in describing the entire drug release curve from HPMC-based matrix tablets is validated by direct fit of power law equation to published data of other authors. A hypothesis based on the nonclassical diffusion of the solutes in the HPMC matrices is used to interpret the successful use of the power law in describing the entire release profile.

Algorithms↗

PubMed2006

Powers of multiple-testing procedures for identification of genes significantly differentially expressed in microarray experiments.

Because of the high operation costs involved in microarray experiments, the determination of the number of replicates required to detect a gene significantly differentially expressed in a given multiple-testing procedure is of considerable significance. Calculation of power/replicate numbers required in multiple-testing procedures provides design guidance for microarray experiments. Based on this model and by choice of a multiple-testing procedure, expression noises based on permutation resampling can be considerably minimized. The method for mixture distribution model is suitable to various microarray data types obtained from single noise sources, or from multiple noise sources. By using the biological replicate number required in microarray experiments for a given power or by determining the power required to detect a gene significantly differentially expressed, given the sample size, or the best multiple-testing method can be chosen. As an example, a single-distribution model of t-statistic was fitted to an observed microarray dataset of 3 000 genes responsive to stroke in rat, and then used to calculate powers of four popular multiple-testing procedures to detect a gene of an expression change D. The results show that the B-procedure had the lowest power to detect a gene of small change among the multiple-testing procedures, whereas the BH-procedure had the highest power. However, all multiple-testing procedures had the same power to identify a gene having the largest change. Similar to a single test, the power of the BH-procedure to detect a small change does not vary as the number of genes increases, but powers of the other three multiple-testing procedures decline as the number of genes increases.

Gene Expression Profiling↗

PubMed1997

Accuracy of Doppler catheter measurements: effect of inhomogeneous beam power distribution on mean and peak velocity.

OBJECTIVES: We sought to determine the effect of inhomogeneous distribution of beam power produced by Doppler catheters on measurements of mean and peak velocity of coronary blood flow. BACKGROUND: Measurements of mean velocity of coronary blood flow by Doppler catheters have significant systematic errors that have not been completely characterized. We hypothesized that one error is the inhomogeneous distribution of the ultrasonic beam power and that this inhomogeneity makes measurements of mean, but not peak, velocity inaccurate. METHODS: We constructed a scaled-up model of a Doppler catheter to allow for accurate measurement of the distribution of beam power by miniature hydrophones. This catheter was placed in a model of coronary blood flow in which the fluid velocity was accurately measured by an external laser Doppler velocimeter. The laser Doppler measurements of mean velocity were compared with the measurements of mean velocity made by the catheter, using fast Fourier transform analysis, both without and with correction for inhomogeneous beam power distribution. Peak velocity measurements were also compared, as predicted from theory, without the need of correction for inhomogeneous beam power distribution. To investigate the clinical relevance of our results, we conducted studies using a clinical Doppler catheter both in a scaled model of coronary flow and in a series of eight patients. In the model and in each patient, we rotated the catheter without changing the axial position to systematically alter the relation of the beam power distribution to the local fluid dynamics. RESULTS: The measurement of beam power distribution revealed significant inhomogeneity. Comparison of the measured mean frequency shifts without correction for inhomogeneities in the distribution yielded a statistically significant difference. After correction for inhomogeneities, there was no statistically significant difference. Also, there was no significant difference for the peak frequency shifts. Rotation of the clinical catheter in the scaled model and in the patients changed the measured mean velocity (average change 18.8% and 20.6%, respectively), but not the measured peak velocity (average change 5.0% and 4.3%, respectively). CONCLUSIONS: For signal analysis using a fast Fourier transform, the inhomogeneous distribution of power of the ultrasonic beam produced by Doppler catheters makes measurements of mean, but not peak, velocity inaccurate. Measurements of peak velocity may therefore prove superior to measurements of mean velocity in estimating the response to pharmacologic intervention and in estimating stenosis severity.

Adult↗

PubMed1998

Assessment of left ventricular contractile state by preload-adjusted maximal power using echocardiographic automated border detection.

OBJECTIVES: We sought to assess the ability of preload-adjusted maximal power measured by echocardiographic automated border detection (ABD) to quantify left ventricular (LV) contractility by determining the effects of alterations in preload, afterload and contractile state. BACKGROUND: Preload-adjusted maximal power can reflect LV contractile state relatively independent of changes in loading conditions. METHODS: Eight anesthetized dogs had placement of aortic electromagnetic flow probes, LV and arterial pressure catheters and inferior vena caval (IVC) occluders; four had placement of thoracic aortic balloon occluders. Echocardiographic ABD measures of cross-sectional area were used as a surrogate for LV volume, and flow was estimated as the first derivative of area with respect to time. Power was calculated as the product of flow and pressure. RESULTS: Preload independence during vena caval occlusions was achieved by preload adjustment (1/[end-diastolic area]3/2). Afterload independence was demonstrated by preload-adjusted maximal power being unaffected by acute increases in LV systolic pressure induced by aortic occlusion. ABD preload-adjusted maximal power reflected changes in contractile state: increasing with dobutamine infusion from 36+/-14 to 70+/-15 mW/cm4 (p < 0.05 vs. control) and decreasing with propranolol infusion from 35+/-13 to 17+/-7 mW/cm4 (p < 0.05 vs. control). These changes were significantly correlated with calculations of preload-adjusted maximal power using aortic flow (r = 0.90, SEE 10.5 mW/cm4) and load-independent measures of end-systolic elastance from pressure-area loops (r = 0.90, SEE 10.6 mW/cm4). Calculations of normalized preload-adjusted maximal power using arterial pressure were also closely correlated with similar calculations using LV pressure (r = 0.99, SEE 3%). CONCLUSIONS: Preload-adjusted maximal power using echocardiographic ABD can predict LV contractile state relatively independent of loading conditions and has potential for clinical application.

Animals↗

PubMed2003

Corneal power after refractive surgery for myopia: contact lens method.

PURPOSE: To clarify the theoretical background of the rigid contact lens overrefraction (CLO) method to determine corneal power after corneal refractive surgery. SETTING: University Eye Clinic, University of Würzburg, Würzburg, Germany. METHODS: Using paraxial geometrical optics, the measurement situation for the contact lens method was analyzed and the definitions of corneal refractive power were reviewed. Based on the theoretical Gullstrand eye, model eyes were constructed, representing 1 emmetropic and 2 myopic eyes (primary refraction -5.21 diopters [D] and -10.25 D, respectively) before and after photorefractive keratectomy and laser in situ keratomileusis. In these eyes, the application of the CLO was mathematically simulated using Gaussian thick-lens optics and commercial ray-tracing software. RESULTS: The CLO method measured neither the equivalent (total) power nor the vertex (back) power of the cornea but rather the quantity 336/R(1C) (R(1C) = anterior corneal radius). Based on these results and the Gullstrand eye, new formulas are proposed to derive the equivalent power and vertex power of the cornea by the CLO method. CONCLUSIONS: Depending on whether intraocular lens calculation formulas are based on equivalent (total) corneal power or vertex corneal power, the respective new formulas for the CLO method should be applied in patients after corneal refractive surgery. An increase in prediction accuracy of the refractive outcome is expected.

Computer Simulation↗

PubMed2003

Adjusting intraocular lens power for sulcus fixation.

PURPOSE: To determine the appropriate correction of predicted intraocular lens (IOL) power for sulcus fixation and to prospectively assess the validity of the obtained correction value in patients having sulcus fixation. SETTING: Department of Ophthalmology, Saiseikai Kurihashi Hospital, Saitama, Japan. METHODS: The postoperative refraction, virtual in-the-bag IOL power for the same postoperative refraction, predicted refraction with an increase in in-the-bag IOL power by 0.50 to 2.00 diopters (D), and effective lens position (ELP) in 30 eyes with a normal axial length after sulcus fixation were retrospectively evaluated. The results were confirmed prospectively in 16 other eyes requiring sulcus fixation. RESULTS: A significant myopic shift (mean 0.78 D +/- 0.47 [SD]) from the predicted refraction occurred after sulcus fixation (P<.0001). The mean virtual IOL power was 1.11 +/- 0.67 D higher than that of the actual sulcus-fixated IOL. The difference between the predicted refraction and the refraction after sulcus fixation was less when the difference in IOL power was 1.00 D. The ELP of the IOLs was 0.75 mm shorter using A-mode measurement and 0.62 mm shorter using back calculation from the theoretical formula with sulcus fixation than with in-the-bag fixation. In the prospective study, there was a small refractive error (mean -0.06 +/- 0.19 D) when the planned IOL power was reduced by 1.00 D for sulcus fixation. CONCLUSION: For sulcus fixation in eyes with a normal axial length, the IOL power should be 1.00 D less than the power for in-the-bag fixation.

Aged↗

PubMed1997

Power Doppler: it's a good thing.

Power Doppler is a new method of ultrasound flow imaging the utility of which is currently under investigation. This technique creates a flow map based on the integrated power of the Doppler spectrum, rather than mean Doppler frequency. Power Doppler imaging is inherently more sensitive in terms of flow detection than standard color Doppler imaging; therefore, power Doppler can display flow for situations in which color Doppler is ineffective and can even display tissue perfusion in highly vascular organs such as the kidneys. Furthermore, power Doppler is not effected by aliasing, nor is it effected by blooming in the same way as color Doppler, which has deleterious effects on color Doppler flow images. The control of blooming with power Doppler may be of great importance in the clinical application of echo-enhancing agents. This review article discusses in detail the technological advantages and disadvantages of power Doppler flow imaging. In addition, it provides a synopsis of the preliminary research studies that have been conducted to date with respect to the clinical applications of power Doppler.

Animals↗

PubMed1998

EEG power spectra of normal preadolescent twins. Gender differences of quantitative EEG maturation.

To determine developmental changes of quantitative EEG maturation, we investigated the electroencephalogram (EEG) power spectra in a sample of 72 pairs of healthy twins (144 subjects, 75 girls and 69 boys) ranging in age from 7-15 years. Main spectral parameters were measured in 16 EEG channels. The statistical significance of differences in the EEG power spectra was compared in relation to age and gender. Gender differences were tested by comparing the EEG parameters of boys and girls in the whole sample and separately in the subgroup of dizygotic twins of the opposite sex (DZO twin pairs). A statistically significant decrease of absolute power occurred with increasing age. A significant redistribution of relative power also appeared in higher age, mainly consisting of a progressive increase of alpha 2 power inversely related to relative alpha 1 and theta power. Polynomial regression models of the relation between alpha 2 and theta relative power with age were best described by a 5-order function. The mean frequency of activity across all spectra also increased with age and was maximal in the eldest subjects (13-15 years), with a significantly higher mean frequency of alpha 2 power in females. Similar age and gender differences were less marked in the subgroup of DZO twin pairs. The topographic distribution of spectral bands in normal subjects suggested an earlier maturation of midparietal or occipital than frontocentral regions, and indicated that the growth spurt does not occur simultaneously over homologous right and left hemisphere regions at the same age.

Adolescent↗

PubMed2001

Electromyographic analysis of a human powered stepper cycle during seated and standing riding.

This study examined the muscular activation patterns produced while riding the Step 'n Go, a tricycle powered by a reciprocating vertical motion and typically used by individuals with cognitive, orthopedic, and neuromuscular conditions. Seven normal, adult subjects were tested at three power levels (75, 100, and 125 W) during seated and standing riding. Eight lower extremity muscles were examined with surface electromyography. Results showed that the major power producing muscles for this device were the gluteus maximus, vastis lateralis and medialis, rectus femoris, and tibialis anterior. At the highest power level, peak and mean muscular activation in these muscles were substantially lower (17-38%) while riding standing compared to seated, and seems to reflect the benefit of body weight for power production while standing. At the lowest power level, the peak and mean muscle activation differences between positions were less remarkable, and in some cases the standing values were greater than seated. This suggests that significant muscular effort was required to maintain standing posture and balance when riding at low power levels. Individuals able to perform vastis lateralis and medialis intensive activities, such as the concentric portion of a squat or using a stepping machine (Stair Master), should be able to comfortably ride the Step 'n Go at low power levels.

Adult↗

PubMed1999

Influence of different factors on the output power transferred into medium by ultrasound.

The influence of several factors (amplitude of ultrasonic waves, external static pressure, temperature and viscosity of medium) acting, either individually or in combination, on the amount of power transferred to a liquid medium during ultrasonication (power output) was measured by calorimetry. At constant amplitude (150 microns) and pressure (200 kPa), the power output decreased as the temperature was raised. The effect of temperature could be compensated by increasing pressure. The magnitude of the increase in power output due to raising the pressure depended on the pressure range and the treatment temperature. At all temperatures and pressures studied, the power output increased exponentially when the amplitude was increased linearly. The magnitude of this power output did not depend on the temperature or pressure of treatment. At 40 degrees C the magnitude of the increase in power output due to increasing the pressure was not influenced by the amplitude of sonic waves. The power output increased as the viscosity of the medium was increased. The magnitude of this effect did not depend on the amplitude but on the static pressure.

Journal Article↗

PubMed2001

Diurnal variations in alpha power density and subjective sleepiness while performing repeated vigilance tasks.

OBJECTIVE: Diurnal variations in EEG activity and subjectively rated sleepiness while performing repeated vigilance tasks were examined. METHODS: Nine diurnally active healthy males underwent repeated vigilance tasks at 08:00, 11:00, 14:00, 17:00 and 20:00 h. An electroencephalogram (EEG) was taken while the subjects performed the tasks with their eyes open. The alpha power spectra (8.6-13.3 Hz) of EEG was integrated. Subjectively rated sleepiness, reaction time and oral temperature were also measured. RESULTS: Significant diurnal variations were found for alpha power, subjectively rated sleepiness and oral temperature. The alpha power was significantly smaller at 08:00 than at 11:00, 14:00, 17:00 and 20:00 h. The subjectively rated sleepiness was significantly larger at 08:00 than at 11:00, 17:00 and 20:00 h. The diurnal variation in alpha power did not correspond to that in subjectively rated sleepiness. On the other hand, repeated vigilance tasks increased the alpha power, subjectively rated sleepiness and reaction time at each time of day. The increase in alpha power was significantly greater at 14:00 than at 08:00 and 20:00 h. CONCLUSIONS: The diurnal variation was found in alpha power while performing vigilance tasks. Furthermore, the increase in alpha power with repetition of the task depended on the time of day.

Adult↗

PubMed2004

Individual analysis of EEG frequency and band power in mild Alzheimer's disease.

OBJECTIVE: This EEG study investigates the role of the cholinergic system, cortico-cortical connections, and sub-cortical white matter on the relationship between individual EEG frequencies and their relative power bands. METHODS: EEGs were recorded at rest in 30 normal elderly subjects (Nold), 60 mild Alzheimer disease (AD) and 20 vascular dementia (VaD) patients, comparable for Mini Mental State Evaluation scores (MMSE 17-24). Individual EEG frequencies were indexed by the theta/alpha transition frequency (TF) and by the individual alpha frequency (IAF) with power peak in the extended alpha range (5-14 Hz). Relative power was separately computed for delta, theta, alpha1, alpha2, and alpha3 bands, on the basis of the TF and IAF. RESULTS: Using normal subjects as a reference, VaD patients showed 'slowing' of alpha frequency (TF-IAF) and lower alpha2 power; Mild AD patients showed lower alpha2 and alpha3 power; delta power was higher in both AD and VaD patients; Theta power was higher only in VaD patients. CONCLUSIONS: Individual analysis of the alpha frequency and power can discriminate mild AD from VaD and normal elderly subjects. SIGNIFICANCE: This analysis may probe pathophysiological mechanisms causing AD and VaD.

Aged↗

PubMed2002

A comparison of peak power in the shoulder press and shoulder throw.

The ability to generate peak power is central for performance in many sports. Currently two distinct resistance training methods are used to develop peak power, the heavy weight/slow velocity and light weight/fast velocity regimes. When using the light weight/fast velocity power training method it was proposed that peak power would be greater in a shoulder throw exercise compared with a normal shoulder press. Nine males performed three lifts in the shoulder press and shoulder throw at 30% and 40% of their one repetition maximum (1RM). These lifts were performed identically, except for the release of the bar in the throw condition. A potentiometer attached to the bar measured displacement and duration of the lifts. The time of bar release in the shoulder throw was determined with a pressure switch. ANOVA was used to examine statistically significant differences where the level of acceptance was set at p < 0.05. Peak power was found to be significantly greater in the shoulder throw at 30% of 1 RM condition [F, (1, 23) = 2.325 p < 0.051 and at 40% of 1 RM [F, (1, 23) = 2.905 p < 0.05] compared to values recorded for the respective shoulder presses. Peak power was also greater in the 30% of 1 RM shoulder throw (510 +/- 103W) than in the 40% of 1 RM shoulder press (471 +/- 96W). Peak power was produced significantly later in the shoulder throw versus the shoulder press. This differing power reflected a greater bar velocity of the shoulder throw at both assigned weights compared with the shoulder press.

Adult↗

PubMedDate not supplied

Power spectra of sternocleidomastoids, splenius capitis, and upper trapezius in oblique exertions.

BACKGROUND CONTEXT: There is relatively little known concerning the spectral profile of the cervical muscles, despite the fact that neck injury and pain are quite prevalent. PURPOSE: The objective of the study was to calculate and study the power spectral characteristics of the sternocleidomastoids, splenii capitis and upper trapezii in anterolateral flexion and posterolateral extension in a ramp contraction. STUDY DESIGN/SETTING: In a laboratory setting experiments were conducted to record surface electromyographic (EMG) data from six cervical muscles and power spectral variables obtained. PATIENT SAMPLE: Forty normal and healthy young adults (21 men, 19 women). OUTCOME MEASURES: Power spectral of EMG signals. METHODS: EMG data for the left and right isometric anterolateral flexion and posterolateral extension were acquired from the sternocleidomastoids, splenii capitis and upper trapezius bilaterally. The subjects were seated in an upright posture and exerted left and right anterolateral flexor and posterolateral extensor efforts from rest to their maximal voluntary contraction in a gradual linear ramp fashion using visual feedback as a guide. The force exerted and the surface EMG data were sampled at 1 kHz at every 10th percentile grade of contraction and the EMG data were subjected to the Fast-Fourier transform analysis. The median frequency (MF), mean power frequency (MPF), peak power and total power of all six cervical muscles were analyzed. RESULTS: In the anterolateral flexion the ipsilateral sternocleidomastoid and splenius capitis had a wider band of frequency, which further widened with increasing grade of contraction. The trapezius did not engage in the same manner or to the same magnitude. The MF of the sternocleidomastoid in the anterolateral flexion in both genders progressively increased, the splenius capitis remained relatively unchanged, and the upper trapezius declined with the increasing grades of contraction. CONCLUSIONS: There is no significant difference between the genders in spectral profile. There is a bilateral symmetry in spectral profile with reference to activity; however, they are significantly different in different activities for the same muscles. With increasing magnitude of contraction power, spectral density distribution increases and the median frequency decreases. These results can serve as a useful reference for painful necks. Restoration of power spectral characteristics may indicate normalcy, which cannot be gleaned by other EMG or force variables.

Adult↗

PubMed2005

Power generation in fed-batch microbial fuel cells as a function of ionic strength, temperature, and reactor configuration.

Power density, electrode potential, coulombic efficiency, and energy recovery in single-chamber microbial fuel cells (MFCs) were examined as a function of solution ionic strength, electrode spacing and composition, and temperature. Increasing the solution ionic strength from 100 to 400 mM by adding NaCl increased power output from 720 to 1330 mW/m2. Power generation was also increased from 720 to 1210 mW/m2 by decreasing the distance between the anode and cathode from 4to 2 cm. The power increases due to ionic strength and electrode spacing resulted from a decrease in the internal resistance. Power output was also increased by 68% by replacing the cathode (purchased from a manufacturer) with our own carbon cloth cathode containing the same Pt loading. The performance of conventional anaerobic treatment processes, such as anaerobic digestion, are adversely affected by temperatures below 30 degrees C. However, decreasing the temperature from 32 to 20 degrees C reduced power output by only 9%, primarily as a result of the reduction of the cathode potential. Coulombic efficiencies and overall energy recovery varied as a function of operating conditions, but were a maximum of 61.4 and 15.1% (operating conditions of 32 degrees C, carbon paper cathode, and the solution amended with 300 mM NaCl). These results, which demonstrate that power densities can be increased to over 1 W/m2 by changing the operating conditions or electrode spacing, should lead to further improvements in power generation and energy recovery in single-chamber, air-cathode MFCs.

Bacteria, Anaerobic↗

PubMed2005

Inverse power potentials: virial coefficients and a general equation of state.

Virial coefficients up to the seventh are calculated for pair potentials depending on inverse powers of separation, for inverse powers from 5 to 80. Unlike the limiting (infinite inverse power) hard-sphere potential, some virial coefficients for finite inverse power potentials are found to be negative. This makes resummation of the virial series for general inverse power potentials more difficult than that for hard spheres, and some alternative resummation methods are presented and compared. A general equation of state is proposed for fluids of particles interacting through inverse power pair potentials, for inverse powers greater than about 10. This includes the "molecular" inverse power of 12, for which the current results support and extend the results of previous studies.

Journal Article↗