Direct Rate Measurements Research Articles

An engineering approach to the 3D printing of K‐Carrageenan/konjac glucomannan hydrogels

SummaryAqueous solutions of Konjac glucomannan (KGM)/κ‐Carrageenan (κ‐C) of different ratios (1:2, 1:5, 1:8 and 1:10) and a fixed κ‐C content of 1.5%, were proposed as a new 3D food printing ink. Their thermo‐responsive behaviour was evaluated by temperature ramp rheological tests. This characterisation allowed for the evaluation of the synergistic effect between KGM and κ‐C and gave indications useful to the printing performance. Both elastic (G′) and loss (G″) moduli were found to increase by increasing the KGM concentration. Samples were printed by controlling the thermally reversible sol/gel transition occurring during the process. Direct pressure and flow rate measurements in the 3D printer were used to obtain the viscosity versus shear rate curves under processing conditions, useful to validate a scaling law relating the printing filament diameter to the relevant process and material properties (inks viscosity and printing pressure). The 3D printing performance of inks was evaluated by means of a novel, integrated score system. The results obtained indicate that aqueous mixtures of KGM/κ‐C can be successfully employed as a base for 3D printing food hydrogels. The use of the score system above outlined proved to be an easy yet efficient tool for the optimisation of the gel composition.

Development of Company-Specific Emission Factors with Confidence Intervals for Natural Gas Customer Meters in Southern California.

Methane is both a significant and short-lived greenhouse gas compared to CO2, and reducing methane emissions from natural gas distribution systems may offer cost-effective reduction opportunities. We report substantial new direct leak rate measurements from customer meter set assemblies (MSAs) in Southern California. In a novel way, emission factors are defined in terms of aboveground Hazardous and Nonhazardous leak categories, which take direct advantage of readily available industry leak data. We also studied leaks that were not detected as part of normal leak survey procedures. As a result, this yields company-specific emission factors that can be used to track progress in reducing methane emissions. This approach also has the advantage of explicitly accounting for the skewed or fat-tail distribution of leak rates by treating high flow rate MSA leaks separately from low flow rate MSA leaks. The Southern California Gas (SoCalGas) methane emission factors, based on 485 leak rate measurements by direct enclosure, were 4.55 (95% confidence interval: 2.32 to 7.14) kg/day for Hazardous leaks, 0.149 (0.119 to 0.183) kg/day for Nonhazardous leaks, and 0.0039 (0.0003 to 0.0198) kg/day for Non-Detected leaks. The percentage of surveyed meters with nondetected leaks was 29.1% (24.3 to 34.6%). Based on a robust Monte Carlo analysis, total leak emissions from MSAs for the SoCalGas system were reduced by 35% based on data from 2015 to 2022. These reductions were attributed to surveying a larger number of MSAs and accelerated leak repair rates. In traditional population-based emission inventories, an individual emission factor for a given asset category is multiplied by the total population of MSAs within the category. This approach simply cannot capture the reduction in leak numbers and methane emissions resulting from leak mitigation and prevention programs.

Optimizing a twin-chamber system for direct ozone production rate measurement

High Ozone Production Rate (OPR) leads to O3 pollution episodes and adverse human health outcomes. OPR observation (Obs-OPR) and OPR modelling (Mod-OPR) have been obtained from observed and modelled peroxy radicals and nitrogen oxides. However, discrepancies between them remind of an imperfect understanding of O3 photochemistry. Direct measurement of OPR (Mea-OPR) by a twin-chamber system emerges. Herein, we optimized Mea-OPR design, i.e., minimizing the chamber surface area to volume ratio (S/V) to 9.8 m−1 from 18 m−1 and the dark uptake coefficient of O3 to 9.9 × 10−9 from 7.1 × 10−8 in the literature. In addition, control experiments further revealed and quantified a photo-enhanced O3 uptake, and therefore recommended an essential correction of Mea-OPR. We finally characterized a measurement uncertainty of ±38% and a detection limit of 3.2 ppbv h−1 (3SD), which suggested that Mea-OPR would be sensitive enough to measure OPR in urban or suburban environments. Further application of this system in urban Beijing during the Beijing 2022 Olympic Winter Games recorded a noontime OPR of 7.3 (±3.3, 1SD) ppbv h−1. These observational results added up to our confidence in future field application of Mea-OPR, to facilitate pollution control policy evaluation and to shed light on O3 photochemistry puzzle.

Direct measurement of spin-flip rates of a self-assembled InAs double quantum dot in single-electron tunneling

Direct measurement of spin-flip rates of a self-assembled InAs double quantum dot in single-electron tunneling

HUBUNGAN LAJU INFILTRASI TERHADAP PERMEABILITAS TANAH DAN MUKA AIRTANAH DI DAERAH DESA TAJUR KECAMATAN CITEUREUP

Infiltration is an important process in a hydrological system and acts as a medium for air infiltration into the soil. The process of infiltration in soil can be influenced by several factors, namely, rainfall, vegetation, land slope, land use, and soil moisture. Apart from this, other factors such as groundwater level and soil permeability also have an influence on the infiltration process, both of which are related to each other in terms of the rate of infiltration or air infiltration into the soil. If the infiltration process is disrupted, it results in the pooling of air on the ground surface, which affects the hydrological system. It is necessary to know how factors such as groundwater levels and soil permeability influence the infiltration rate. Based on this, the aim of this research is to determine the relationship. between infiltration rate, groundwater level, and soil permeability and their influence. The research method was carried out by taking data from direct groundwater level measurements and infiltration rate measurements, as well as samples for soil permeability analysis. Then an interpretation of the data obtained is carried out and presented in a map of the infiltration zone and soil permeability zone. The research area in Tajur Village has 2 infiltration zones, namely the slow-medium zone and the medium zone with medium and rather fast soil permeability and low-medium groundwater depth.

A deep reservoir for hydrogen drives intense degassing in the Bulqizë ophiolite

Deep crustal production of hydrogen (H 2 ) is a potential source of primary energy if recoverable accumulations in geological formations are sufficiently large. We report direct measurements of an elevated outgassing rate of 84% (by volume) of H 2 from the deep underground Bulqizë chromite mine in Albania. A minimum of 200 tons of H 2 is vented annually from the mine’s galleries, making it one of the largest recorded H 2 flow rates to date. We cannot attribute the flux solely to the release of paleo-fluids trapped within the rocks or to present-day active and pervasive serpentinization of ultramafic rocks; rather, our results demonstrate the presence of a faulted reservoir deeply rooted in the Jurassic ophiolite massif. This discovery suggests that certain ophiolites may host economically useful accumulations of H 2 gas.

Anomalous cross-field transport in a Hall thruster inferred from direct measurement of instability growth rates.

The contribution of the electron drift instability to anomalous electron transport is experimentally assessed in a Hall effect discharge. The transport is represented by an anomalous collision frequency, which is related through quasilinear theory to the energy and growth rate of the instability. The wave energy is measured directly with ion saturation probes, while estimates of the growth rate are employed based on both linearized theory and direct measurement. The latter measurement is performed with a bispectral analysis method. The wave-driven collision frequency is compared to measurements of the actual collision frequency inferred from a method based on laser-induced fluorescence. It is found that estimates for transport using linearized theory for the growth differ by over an order of magnitude from the actual anomalous collision frequency in the plasma. The wave-driven anomalous collision frequency with measured growth, however, is shown to agree with the electron collision frequency in magnitude and capture aspects of the trends in spatial variation. This result demonstrates experimentally that wave-driven effects ultimately can explain the observed cross-field transport in these devices. The implications of this finding are discussed in the context of the key lengthscales that drive the transport as well as the implications identifying reduced fidelity models that could be used to predict anomalous collision frequency.

The first direct measurements of ventilatory flow and oxygen utilization after exhaustive exercise and voluntary feeding in a teleost fish, Oncorhynchus mykiss.

A new "less invasive" device incorporating an ultrasonic flow probe and a divided chamber, but no stitching of membranes to the fish, was employed to make the first direct measurements of ventilatory flow rate (V̇w) and % O2 utilization (%U) in juvenile rainbow trout (37g, 8ºC) after exhaustive exercise (10-min chasing) and voluntary feeding (2.72% body mass ration). Under resting conditions, the allometrically scaled V̇w (300mlkg-1min-1 for a 37-g trout = 147mlkg-1min-1 for a 236-g trout exhibiting the same mass-specific O2 consumption rate, ṀO2) and the convection requirement for O2 (CR = 4.13 L mmol-1) were considerably lower, and the %U (67%) was considerably higher than in previous studies using surgically attached masks or the Fick principle. After exhaustive exercise, V̇w and ṀO2 approximately doubled whereas frequency (fr) and %U barely changed, so increased ventilatory stroke volume (Vsv) was the most important contributor to increased ṀO2. CR declined slightly. Values gradually returned to control conditions after 2-3h. After voluntary feeding, short-term increases in V̇w, Vsv and ṀO2 were comparable to those after exercise, and fr again did not change. However, %U increased so CR declined even more. The initial peaks in V̇w, Vsv and ṀO2, similar to those after exercise, were likely influenced by the excitement and exercise component of voluntary feeding. However, in contrast to post-exercise fish, post-prandial fish exhibited second peaks in these same parameters at 1-3h after feeding, and %U increased further, surpassing 85%, reflecting the true "specific dynamic action" response. We conclude that respiration in trout is much more efficient than previously believed.

Experimental Evidence and Mechanistic Description of the Phenolic H-Transfer to the Cu2O2 Active Site of oxy-Tyrosinase.

Tyrosinase is a ubiquitous coupled binuclear copper enzyme that activates O2 toward the regioselective monooxygenation of monophenols to catechols via a mechanism that remains only partially defined. Here, we present new mechanistic insights into the initial steps of this monooxygenation reaction by employing a pre-steady-state, stopped-flow kinetics approach that allows for the direct measurement of the monooxygenation rates for a series of para-substituted monophenols by oxy-tyrosinase. The obtained biphasic Hammett plot and the associated solvent kinetic isotope effect values provide direct evidence for an initial H-transfer from the protonated phenolic substrate to the Cu2O2 core of oxy-tyrosinase. The correlation of these experimental results to quantum mechanics/molecular mechanics calculations provides a detailed mechanistic description of this H-transfer step. These new mechanistic insights revise and expand our fundamental understanding of Cu2O2 active sites in biology.

Direct gamma dose rate measurement and assessment of excess lifetime cancer risk.

In this study, in some neighborhoods in Kahramanmaraş province of Turkey, indoors and outdoors direct gamma dose rate measurements have been done. All of the gamma dose rate measurements have been made at ground level and at the height of 1m from the ground. The median values of the gamma dose rates on the ground and 1m above the ground indoors are 70.34±7.74 and 49.53±5.39nGy h-1, respectively. Outdoor measurements have been carried out on both soil and asphalt floors. The average values of gamma dose rate on the ground and at a height of 1m outdoors (soil floor) are 68.16±7.49 and 53.50±5.88nGy h-1, respectively. The mean values of gamma dose rate on the ground and 1m above the ground outdoors (asphalt floor) are 61.63±6.77 and 48.69±5.35nGy h-1, respectively. Indoor and outdoor average gamma dose rates are below the mean world. In addition, using the measured gamma dose rate values, annual effective dose equivalent (AEDE) and excess lifetime cancer risk (ELCR) for adults have been calculated. The total AEDE and ELCR (on soil floors and indoors at 1m above ground level) are 0.31±0.03mSv y-1 and 1.08±0.10×10-3, respectively. The total AEDE and ELCR (on asphalt floors and indoors at 1m above ground level) are 0.30±0.03mSv y-1 and 1.06±0.10×10-3, respectively. The AEDE and ELCR for adults living in the neighborhoods within the scope of the study in Kahramanmaraş city center within 1y are lower than the average world.

The Effect of the Human Brainstem Myelination on Gait Speed in Normative Aging.

The brainstem functions as a relay and integrative brain center and plays an essential role in motor function. Whether brainstem tissue deterioration, including demyelination, affects motor function has not been studied. Understanding the potential relationship between brainstem demyelination and motor function may be useful for the early diagnosis of neurodegenerative diseases and to understand age-related gait impairments that have no apparent cause. In this work, we investigated the associations between rapid or usual gait speeds, as integrative measures of motor function, and cerebral myelin content. In 118 individuals (age 22-94 years) free of neurodegenerative diseases or cognitive impairment, myelin content was assessed as the myelin water fraction, a direct magnetic resonance imaging measure of myelin content, and longitudinal and transverse relaxation rates (R1 and R2), which are sensitive magnetic resonance imaging measures of myelin content. Our results indicate that participants with lower usual or rapid gait speed exhibited lower values of myelin water fraction and R1 in the main brainstem regions, which were more evident and statistically significant in the midbrain. In contrast, we found no significant associations between gait speeds and R2, an expected result because various physiological factors confound R2. These original findings provide evidence that the level of brainstem myelination may affect gait performance among cognitively unimpaired adults who are free from any clinically detectable neurodegenerative diseases. Further studies are needed to understand the longitudinal changes in brainstem myelination with aging and neurodegenerative diseases, including Alzheimer's disease and Parkinson's disease.

Hypertensive Adults Exhibit Lower Myelin Content: A Multicomponent Relaxometry and Diffusion Magnetic Resonance Imaging Study.

It is unknown whether hypertension plays any role in cerebral myelination. To fill this knowledge gap, we studied 90 cognitively unimpaired adults, age range 40 to 94 years, who are participants in the Baltimore Longitudinal Study of Aging and the Genetic and Epigenetic Signatures of Translational Aging Laboratory Testing to look for potential associations between hypertension and cerebral myelin content across 14 white matter brain regions. Myelin content was probed using our advanced multicomponent magnetic resonance relaxometry method of myelin water fraction, a direct and specific magnetic resonance imaging measure of myelin content, and longitudinal and transverse relaxation rates (R1 and R2), 2 highly sensitive magnetic resonance imaging metrics of myelin content. We also applied diffusion tensor imaging magnetic resonance imaging to measure fractional anisotropy, mean diffusivity, radial diffusivity, and axial diffusivity values, which are metrics of cerebral microstructural tissue integrity, to provide context with previous magnetic resonance imaging findings. After adjustment of age, sex, systolic blood pressure, smoking status, diabetes status, and cholesterol level, our results indicated that participants with hypertension exhibited lower myelin water fraction, fractional anisotropy, R1 and R2 values and higher mean diffusivity, radial diffusivity, and axial diffusivity values, indicating lower myelin content and higher impairment to the brain microstructure. These associations were significant across several white matter regions, particularly in the corpus callosum, fronto-occipital fasciculus, temporal lobes, internal capsules, and corona radiata. These original findings suggest a direct association between myelin content and hypertension and form the basis for further investigations including longitudinal assessments of this relationship.

Wellhead optimization of the demulsification of water-in-oil emulsion using response surface methodology

Stable emulsion formation is a common but undesirable phenomenon during enhanced oil recovery processes. Although much research has been conducted to examine the mechanisms of emulsification and demulsification, most of the studies were conducted offline on a laboratory scale and were aimed to optimize the separation-efficiency, which neither represents the actual well situation nor gives a direct measure of the oil recovery rate. Therefore, this study aims to conduct wellhead optimization of the demulsification process, targeting the enhancement in the oil production rate. The effect of the demulsifier dosage and the gas-lift rate on the production rate was investigated online, and the process was optimized using response surface methodology (RSM). The results revealed that both factors and their interaction significantly affected the production rate and presented P-values <0.05. A predictive model was developed for the production rate with R 2 value of 95.46% indicating the high accuracy of the model. The optimum conditions of 250 MSCF/day gas-lift rate and 25 Qt/day demulsifier dosage corresponding to 40 BOPD production rate were achieved. These conditions were verified online, with 0.25% error compared to the predicted value, confirming the excellent accuracy and reliability of the wellhead optimization results.

Pattern and trends of the total and age-specific fertility rates during 1990–2018 in Pakistan

BackgroundPakistan has an inadequate vital event registration system, leading to fewer than half of all births being registered, and this issue is further exacerbated by systematic recall errors and omission of births. This study aims to evaluate direct and indirect methods of fertility estimation to analyze the trends and patterns of fertility rates in Pakistan from 1990 to 2018.Design/methodology/approachIndirect methods are utilized in this study to evaluate the direction and extent of changes in total and age-specific fertility rates, and these findings are compared to direct estimates. The study draws data on livebirths from four waves of the Pakistan Demographic and Health Survey that took place between 1990 and 2018. To ensure the quality of data, graphical methods and Whipple and Myers indices are employed. Additionally, the Brass Relational Gompertz model was used to analyze the data.ResultsThe Relational Gompertz model revealed that total fertility rates (TFRs) were higher than direct estimates by 0.4 children and age-specific fertility rates (ASFR) were higher for all age groups except the oldest. The difference was more significant among younger women aged 15–24, and less so for age groups 29 and above. The gap in estimated fertility between direct and indirect methods decreased with age.ConclusionThe indirect method is an invaluable tool in situations where direct measurement of fertility rates is challenging or impossible. By utilizing this method, policymakers can gain important insights into the fertility patterns and trends of a population, which is crucial for making informed decisions on fertility planning.

Size-fractionated N2 fixation off the Changjiang Estuary during summer.

Recent evidence has shown active N2 fixation in coastal eutrophic waters, yet the rate and controlling factors remain poorly understood, particularly in large estuaries. The Changjiang Estuary (CE) and adjacent shelf are characterized by fresh, nitrogen-replete Changjiang Diluted Water (CDW) and saline, nitrogen-depletion intruded Kuroshio water (Taiwan Warm Current and nearshore Kuroshio Branch Current), where N2 fixation may be contributed by different groups (i.e., Trichodesmium and heterotrophic diazotrophs). Here, for the first time, we provide direct measurement of size-fractionated N2 fixation rates (NFRs) off the CE during summer 2014 using the 15N2 bubble tracer method. The results demonstrated considerable spatial variations (southern > northern; offshore > inshore) in surface and depth-integrated NFRs, averaging 0.83 nmol N L-1 d-1 and 24.3 μmol N m-2 d-1, respectively. The highest bulk NFR (99.9 μmol N m-2 d-1; mostly contributed by >10 μm fraction) occurred in the southeastern East China Sea, where suffered from strong intrusion of the Kuroshio water characterized by low N/P ratio (<10) and abundant Trichodesmium (up to 10.23 × 106 trichomes m-2). However, low NFR (mostly contributed by <10 μm fraction) was detected in the CE controlled by the CDW, where NOx concentration (up to 80 μmol L-1) and N/P ratio (>100) were high and Trichodesmium abundance was low. The >10 μm fraction accounted for 60% of depth-integrated bulk NFR over the CE and adjacent shelf. We speculated that the present NFR of >10 μm fraction was mostly supported by Trichodesmium. Spearman rank correlation indicated that the NFR was significantly positively correlated with Trichodesmium abundance, salinity, temperature and Secchi depth, but was negatively with turbidity, N/P ratio, NOx, and chlorophyll a concentration. Our study suggests that distribution and size structure of N2 fixation off the CE are largely regulated by water mass (intruded Kuroshio water and CDW) movement and associated diazotrophs (particularly Trichodesmium) and nutrient conditions.

Gamma-ray measurements for inertial confinement fusion applications

High-energy γ rays generated from inertial confinement fusion (ICF) experiments have become an important signature for studying the dynamics of implosion processes. Due to their high-energy and penetrating nature, γ rays are the most unperturbed fusion products, which can preserve the original birth information of the fusion process. Fusion γ rays provide a direct measure of nuclear reaction rates (unlike x rays) without being compromised by Doppler spreading (unlike neutrons). However, unambiguous γ-ray measurements for ICF study further required a decade-long period of technological development, which included a deepening understanding of fusion γ-ray characteristics and innovations in instrument performance. This review article introduces the production mechanism of the prompt and secondary γ rays and various ICF performance parameters (e.g., bang time and burn width), which can be derived from γ-ray measurement. A technical overview will be followed by summarizing γ-ray detectors fielded or proposed, especially for high-yield ICF experiments at the Omega Laser Facility and National Ignition Facility. Over the past few years, γ-ray diagnostic technologies have been extended beyond ICF research. A few examples of non-ICF applications of γ-ray detectors are introduced at the end of this article.

Assessment of Musculoskeletal Pain and Physical Demands Using a Wearable Smartwatch Heart Monitor among Precast Concrete Construction Workers: A Field Case Study

This study aimed to quantify musculoskeletal symptoms/pain and characterize the physical demands at work and outside of work among precast concrete workers. Direct heart rate (HR) measurements and self-reported activity levels were used to estimate the physical demands. A total of 27 precast construction workers participated in a survey, and 21 wore a HR monitor smart watch for seven days. The HR data were parsed in minutes associated with occupational and nonoccupational physical activity. Correlation analysis and multivariate regression models were conducted to assess the associations between direct measured physical activity with self-reported physical activity, body mass index (BMI), years of work, smoking, and Borg ratings of perceived exertion (RPE). Approximately half of the participants experienced musculoskeletal symptoms in the last seven days and moderate functional limitations in carrying out activities of daily living (ADLs). The regression model revealed a positive relationship between direct measured moderate occupational physical activity (OPA) and the Borg RPE. Furthermore, an inverse association was found with BMI, smoking status, and years of work. The workers accrued a median of 415 min of moderate OPA per week. The findings showed a high amount of moderate OPA minutes per week and musculoskeletal issues among the precast concrete workers.

Nitrite cycling in the primary nitrite maxima of the eastern tropical North Pacific

Abstract. The primary nitrite maximum (PNM) is a ubiquitous feature of the upper ocean, where nitrite accumulates in a sharp peak at the base of the euphotic zone. This feature is situated where many chemical and hydrographic properties have strong gradients and the activities of several microbial processes overlap. Near the PNM, four major microbial processes are active in nitrite cycling: ammonia oxidation, nitrite oxidation, nitrate reduction and nitrite uptake. The first two processes are mediated by the nitrifying archaeal/bacterial community, while the second two processes are primarily conducted by phytoplankton. The overlapping spatial habitats and substrate requirements for these microbes have made understanding the formation and maintenance of the PNM difficult. In this work, we leverage high-resolution nutrient and hydrographic data and direct rate measurements of the four microbial processes to assess the controls on the PNM in the eastern tropical North Pacific (ETNP). The depths of the nitrite maxima showed strong correlations with several water column features (e.g., top of the nitracline, top of the oxycline, depth of the chlorophyll maximum), whereas the maximum concentration of nitrite correlated weakly with only a few water column features (e.g., nitrate concentration at the nitrite maximum). The balance between microbial production and consumption of nitrite was a poor predictor of the concentration of the nitrite maximum, but rate measurements showed that nitrification was a major source of nitrite in the ETNP, while phytoplankton release occasionally accounted for large nitrite contributions near the coast. The temporal mismatch between rate measurements and nitrite standing stocks suggests that studies of the PNM across multiple timescales are necessary.

PROBLEMS OF MEASURING LOW FEED RATES OF METAL CUTTING EQUIPMENT

The article is dedicated to the problem formulation of improving the method for measuring low feed rates in metal-cutting machines during finishing operations by using direct speed measurement sensors. The goal of the work is to review the issue of measuring low feed rates in blade machining in order to assess and minimize the uncertainties of feed rate measurements. The necessity of measurements and subsequent analysis of feed rate instabilities in metal-cutting machines within the range of 0 to 20 mm/min is demonstrated. It is shown that the uneven movement of machine tool elements can be a result of clearances in movable joints and overcoming friction forces in these clearances. The influence of the adaptive control system of the machine tool drive on the unevenness of feed rate is also presented. The effect on the unevenness of feed rate of different types of drives is described, including stepper motors, hydraulic and pneumatic drives, asynchronous motors with frequency converters, and servo motors. The main components of uncertainty arising from the indirect method of velocity measurement are described, related to uncertainties in time and distance measurement, errors in approximation during instantaneous velocity calculation, as well as errors associated with the discretization of time and distance measurements. Methods of direct feed rate measurement are discussed. It is shown that it is not possible to use sensors utilizing the Doppler effect for measuring small feed rates. It is noted that existing designs of magnetic velocity sensors have significant nonlinearity, which cannot be eliminated by adjusting measurement results. Limitations of known sensors regarding the length of the path on which the feed rate can be measured are specified. A promising direction for research on improving the method of direct measurement of small feed rates in metal cutting machines is identified.

A Direct Measurement of Galaxy Major and Minor Merger Rates and Stellar Mass Accretion Histories at Z < 3 Using Galaxy Pairs in the REFINE Survey

We measure the role of major and minor mergers in forming the stellar masses of galaxies over redshifts 0 < z < 3 using a combination of ∼3.25 deg2 of the deepest ground-based near-infrared imaging taken to date (Ultra Deep Survey, Ultra-VISTA, and VIDEO) as part of the collated REFINE survey. We measure the pair fraction and merger fractions for galaxy mergers of different mass ratios, and quantify the merger rate with newly measured timescales derived from the Illustris simulation as a function of redshift and merger mass ratio. For a M * > 1011 M ⊙ selection, we find that over 0 < z < 3 major mergers with mass ratios greater than 1:4 occur times on average, while minor mergers down to ratios of 1:10 occur on average times per galaxy. We also quantify the role of major and minor mergers in galaxy formation, whereby the increase in mass due to major mergers is while minor mergers account for an increase of using a M * > 1011 M ⊙ selection. We thus find that major mergers add more stellar mass to galaxies than minor mergers over this epoch. Overall, mergers will more than double the mass of massive galaxies over this epoch when selecting by stellar mass. We however find a lower increase in stellar mass when selecting by a constant number density. Finally, we compare our results to simulations, finding that minor mergers are overpredicted in Illustris and in semi-analytical models, suggesting a mismatch between observations and theory in this fundamental aspect of galaxy assembly.