Energy Gradient Research Articles

Starting inflation from inhomogeneous initial conditions with momentum

We investigate the circumstances under which cosmic inflation can arise from very inhomogeneous initial conditions using numerical relativity simulations. Previous studies have not considered cases with non-zero momentum density due to technical challenges with solving the coupled Einstein constraint equations. Here we address these, introducing and comparing several different ways of constructing cosmological initial conditions with inhomogeneous scalar field and time derivative profiles. We evolve such initial conditions with large inhomogeneities in both single- and two-field inflationary models. We study cases where the initial gradient and kinetic energy are much larger than the inflationary energy scale, and black holes can form, as well as cases where the initial scalar potential energy is comparable, as in scenarios where inflation occurs at nearly Planckian densities, finding large-field inflation to be generally robust. We consider examples of initial conditions where a large scalar field velocity towards non-inflationary values would prevent inflation from occurring in the homogeneous case, finding that the addition of large gradients in the scalar field can actually dilute this effect, with the increased expansion and non-vanishing restoring force leading to inflation.

Unlocking energy potential: Decarbonizing water reclamation plants with salinity gradient energy recovery

Climate change, together with the ecological droughts suffered by a large part of the European Union's territory, calls for joint environmental solutions. In this regard, water reclamation is a promising way to alleviate the pressure on existing water resources. However, reuse strategies are penalized by the extra energy consumed in urban wastewater treatment plants (UWWTPs), facilities mainly powered by fossil fuels. The opportunity to integrate renewable sources of energy into the energy-intensive UWWTPs holds great promise towards decarbonization of the sector. In this context, the energy harvested from a Salinity Gradient (SGE) has attracted great interest in the last decade. This work aims at the analysis of opportunity of implementing integrated processes for water reclamation and SGE recovery in the coastal EU UWWTPs. According to the selection criteria, a total of 281 potential sites located across eighteen coastal countries of the EU have been inventoried attending to the current state of the art. The water reclamation potential has been estimated at 3.7 million m3/day. As a consequence, the environmental burdens of the reclamation process could result in the reduction of 1.5·105 t CO2/year. The Mediterranean region, highly affected by hydrological drought, has proved to be a hot spot for water reclamation, with the highest number of plants inventoried in the study and a predicted potential for SGE harvesting of 60 Wh/m3 of reclaimed water. These results highlight a niche of opportunities to encourage water reclamation, avoid water bodies' degradability due to effluent discharge and the further decarbonization of reclamation processes.

The effect of the third component on high performance ternary organic solar cells: A review

AbstractIn recent years, with the continuous development of photoactive layer material, the power conversion efficiency (PCE) of bulk heterojunction (BHJ) binary organic solar cells (BOSCs) has been significantly improved. However, it is difficult for BOSCs to maximize the effective utilization of the wide spectrum of solar energy, limiting the further improvement of PCE. Adding a third component to BOSCs that constructing ternary organic solar cells (TOSCs) is an effective method to broaden the absorption spectrum of BOSC, match the gradient energy level, and regulate the morphology of the active layer. Constructing TOSCs can not only effectively improve the device performance, but also maintain the advantages of easy‐to‐fabricate single‐junction device structures. In this review, we first introduced the basic working mechanism of TOSCs. Then based on the working mechanism, we comprehensively reviewed the latest research results of TOSCs, and analyzed the effects of the third component on the microscopic morphology of the active layer, photovoltaic performance and device stability. Finally, we systematically summarized the role of the third component in TOSCs and proposed some future development trends of TOSCs, such as designing and synthesizing more economical, green, and environmentally friendly TOSCs that towards the commercial application in the future.

Widespread use of proton-pumping rhodopsin in Antarctic phytoplankton

Photosynthetic carbon (C) fixation by phytoplankton in the Southern Ocean (SO) plays a critical role in regulating air-sea exchange of carbon dioxide and thus global climate. In the SO, photosynthesis (PS) is often constrained by low iron, low temperatures, and low but highly variable light intensities. Recently, proton-pumping rhodopsins (PPRs) were identified in marine phytoplankton, providing an alternate iron-free, light-driven source of cellular energy. These proteins pump protons across cellular membranes through light absorption by the chromophore retinal, and the resulting pH energy gradient can then be used for active membrane transport or for synthesis of adenosine triphosphate. Here, we show that PPR is pervasive in Antarctic phytoplankton, especially in iron-limited regions. In a model SO diatom, we found that it was localized to the vacuolar membrane, making the vacuole a putative alternative phototrophic organelle for light-driven production of cellular energy. Unlike photosynthetic C fixation, which decreases substantially at colder temperatures, the proton transport activity of PPR was unaffected by decreasing temperature. Cellular PPR levels in cultured SO diatoms increased with decreasing iron concentrations and energy production from PPR photochemistry could substantially augment that of PS, especially under high light intensities, where PS is often photoinhibited. PPR gene expression and high retinal concentrations in phytoplankton in SO waters support its widespread use in polar environments. PPRs are an important adaptation of SO phytoplankton to growth and survival in their cold, iron-limited, and variable light environment.

Growth Reduction of Similarity-Transformed Electronic Hamiltonians in Qubit Space.

Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to "pre-process" the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the similarity-transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the complete Pauli group for N qubits which minimizes the onset of new terms in the transformed Hamiltonian while facilitating substantial energy lowering. We benchmark the growth-mitigating generator selection technique for ground state energy estimations applied to models of the H4, N2, and H2O molecular systems. It is found that utilizing a selection procedure which obtains the growth-minimizing generator from the set of operators with the maximal energy gradient is the most competitive approach to reducing the onset of Hamiltonian terms while achieving systematic energy lowering of the reference state.

Interfacial oxygen vacancies and energy-level engineering on CeO2-PPy-rGO nanocomposites towards boosted NO2 sensor performance

Monitoring of harmful nitrogen dioxide (NO2) gases is imperative for our health and environmental protection. The room-temperature operating NO2 gas sensors still suffer a limited sensitivity and slow response/recovery rate. In this work, novel CeO2-PPy-rGO nanocomposites were synthesized for improved NO2 sensing performance. The decoration of rGO introduced additional oxygen vacancies on CeO2 for enhancing the sensor response. PPy acted as a buffer layer of energy level connecting CeO2 and rGO components and promoted the response and recovery rate. The designed sensor demonstrated ppb-level NO2 detection in p-type sensing behaviors with rapid response/recovery characteristics as expected at room temperature (RT). The hybrid sensor also showed excellent selectivity, long-term stability and extremely low detection limit toward NO2. The significantly enhanced sensing properties to NO2 could be attributed to activity enhancement, a gently gradient energy level and π-π stacking between rGO and PPy. This study offers a perspective on the design of CeO2-based gas sensors for NO2 detection at RT.

Дослідження показників якості організації дорожнього руху в умовах міста методом GPS-треків

The choice of rational quality criteria for the organization of road traffic in cities is an urgent task for scientists in the field of road transport, as it directly affects the effectiveness of activities in the field of ensuring the safety and comfort of car traffic in urban conditions. Depending on the goals of the analysis, the complexity of the network, and technical capabilities, the quality of traffic management can be assessed by indicators of the economic efficiency of the transport process, the level of accidents, environmental safety, social attractiveness, etc. The modern level of development of geo-information technologies allows for constant monitoring of the vehicle's speed mode. To obtain characteristics of the quality of traffic organization, experimental studies were conducted on a section of the street-road network of the city of Kharkiv, which corresponds to a typical route of personal transport from a remote sleeping area to the central part of the city.
 As a result of data processing of the GPS track, a histogram of the distribution of instantaneous speed and graphs of the car’s movement in the coordinates “time-distance”, “time-speed”, "distance-speed” were built, which allow you to visually assess the mode of movement along the entire route and determine potential "bottlenecks". Such spatio-temporal characteristics as average technical speed, specific time in motion, specific idle time, as well as energy indicators of the quality of traffic management were also calculated: acceleration noise, speed gradient, energy gradient. After dividing the experimental route into separate kilometer sections, changes in the characteristics of the quality of traffic organization, as it approached the city center, were analyzed. On the first half of the route, when moving along the main street, the instability of the speed regime was observed due to stops and idling in the zone of regulated intersections. The presence of a trend towards a decrease in the average technical speed when approaching the city center is explained by an increase in the loading of VDM within the central business part of the city and, as a result, the appearance of additional traffic delays. As we approached the city center, the specific time in motion increased with a slight increase in the specific idle time, and an increase in the speed gradient was also observed with a slight decrease in the energy gradient.

Interacting Quantum Atoms and Multipolar Electrostatic Study of XH···π Interactions.

The interaction energies of nine XH···π (X = C, N, and O) benzene-containing van der Waals complexes were analyzed, at the atomic and fragment levels, using QTAIM multipolar electrostatics and the energy partitioning method interacting quantum atoms/fragment (IQA/IQF). These descriptors were paired with the relative energy gradient method, which solidifies the connection between quantum mechanical properties and chemical interpretation. This combination provides a precise understanding, both qualitative and quantitative, of the nature of these interactions, which are ubiquitous in biochemical systems. The formation of the OH···π and NH···π systems is electrostatically driven, with the Qzz component of the quadrupole moment of the benzene carbons interacting with the charges of X and H in XH. There is the unexpectedly intramonomeric role of X-H (X = O, N) where its electrostatic energy helps the formation of the complex and its covalent energy thwarts it. However, the CH···π interaction is governed by exchange-correlation energies, thereby establishing a covalent character, as opposed to the literature's designation as a noncovalent interaction. Moreover, dispersion energy is relevant, statically and in absolute terms, but less relevant compared to other energy components in terms of the formation of the complex. Multipolar electrostatics are similar across all systems.

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States.

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

Effects of multivalent ions on hydrogen production from the salinity gradient between desalination concentrated brine and river by reverse electrodialysis

In order to simultaneously produce hydrogen and reduce the salinity of concentrated wastewater (brine) from the desalination plant, a lab-scale reverse electrodialysis (RED) hydrogen production system driven by salinity gradient energy is designed and its performance is experimentally studied. The energy conversion of the RED system is found affected by the ionic compositions of the desalination concentrated brine (DCB). The effects of ionic types (multivalent cation, anion, and phosphorous salt) and ionic concentration (from 0.01 to 0.05 M) and pH of DCB (from 5 to 11) on the hydrogen production are investigated. The results show that the existence of multivalent ions in brine significantly degrade the capability of output voltage and hydrogen production of the RED system. Compared to the control group, the additions of 0.05 mol·L−1 NaBr and 0.05 mol·L−1 FeCl3 into the simulated brines lead to the output voltage drops of 29 % and 60 %, respectively, when the current is maintained at 0.2A. Additionally, the experiment yields an MHP of 128 mL·h−1 at the current of 0.3A. Generally, the performances of the RED stack can be improved as increasing the pH of an acidic DCB, but declined as the increasing the pH of an alkaline DCB.

Unlocking synergies between seawater desalination and saline gradient energy: Assessing the environmental and economic benefits for dual water and energy production

The global scarcity of fresh water has increased the desalination systems' importance. Although these systems face certain limitations, significant efforts are being made using renewable energy sources like Saline Gradient Energy (SGE). This led to the emergence of two technologies: Pressure Retarded Osmosis (PRO) and Reversal Electrodialysis (RED). Hence, this innovative study aims to contrast the potential environmental and economic benefits by performance of PRO and RED integration into desalinating seawater by Reverse Osmosis (SWRO). We comprehensively assessed their life cycle using SimaPro® software and conducted a stochastic economic evaluation to achieve this. For the calculation basis, the systems were dimensioned using Wave® software and theoretical-analytical methods based on technical literature. Our findings revealed SWRO-PRO is cheaper (1.49 USD/m3), less energy-intensive (4.602 kWh/m3), and more environmentally friendly than SWRO (emission reductions in the following categories: 10.31% human health, 11.79% ecosystem quality, and 11.44% natural resources depletion). SWRO was the second-best option with moderate costs (1.53 USD/m3), energy requirement (5.569 kWh/m3), and environmental impacts, while SWRO-RED was the least favorable, with higher costs (1.83 USD/m3), energy consumption (5.573 kWh/m3), and environmental impacts (increases of 22.20%, 21.02%, 15.2%, 22.2% of mentioned categories, respectively). PRO integration represented an enhancement, and despite lower benefits, RED maintains a substantial future potential. Thus, this study is a unique holistic approach that integrates environmental and economic considerations and endeavors to revolutionize our understanding of synergistic water-energy systems. Therefore, this pioneering research could pave the way to address global water scarcity and clean energy challenges.

Training feedforward neural nets in Hopfield-energy-based configuration: A two-step approach

We introduce Hopfield-Energy-Based Learning, a general learning framework that is inspired by energy-based models, to train feedforward neural nets. Our approach includes two training phases applied iteratively: first, the minimization of the internal energy, which captures dependencies between input samples and network parameters, is carried out in an unsupervised manner; second, the problem-dependent supervised external energy (e.g., cross-entropy loss) combined with partially reversed internal energy gradients are back-propagated in a standard manner. The intuition is that the first stage helps parameters to settle into the state that simply partitions data into clusters; while in the second stage, the network is allowed to deviate from that clustering a bit (hence gradient reversal) in order to converge to parameters that ultimately perform well on the task at hand. Notably, the data used for the two steps might not be one and the same (e.g., can come from different domains) and the approach naturally tailors itself to solve unsupervised domain adaptation problems without adopting any distribution alignment techniques. We also show that the proposed training strategy substantially improves the performance of several ConvNets on standard supervised classification tasks; showing improvements of at least 1.2% (2.64% on CIFAR-10, 4.5% on CIFAR-100, and 1.35% on ImageNet). Our formulation is general, performs well in practice, and holds promise for scenarios where labeled data is limited.

Effects of Cold Plasma on the Excitation of Internally Driven ULF Waves by Ring Current Ions Based On the Magnetosphere‐Ionosphere Coupled Model

AbstractInternally driven Pc4‐5 waves are excited in the plasmaspheric drainage plume (PDP) and near the plasmapause. The excitation of ultralow frequency (ULF) waves was investigated by using the magnetosphere‐ionosphere coupled model between Geospace Environment Modeling System for Integrated Studies‐Ring Current (GEMSIS‐RC) and GEMSIS‐POTential solver (GEMSIS‐POT). In order to investigate the effects of cold plasma on the wave excitation, the simulation code to describe the dynamics of cold plasma was included in the model. The model can reproduce the shrink of the plasmasphere on the nightside and the formation of the PDP on the dayside. First, fundamental Pc5 waves are excited through the drift resonance on the dayside. The waves are caused by positive energy gradient of ion phase space density (PSD) at 50–130 keV. Second harmonic waves (drift‐bounce resonance) are generated outside the plasmapause. These two types of ULF waves are also seen in the case of constant density. Unlike the case of constant density, localized eastward propagating Pc4 waves (drift resonance) are seen on the dawnside associated with the azimuthal density gradient. The azimuthal wave number of Pc4 waves is about 70 and anti‐earthward gradient of PSD about 10 keV contributes to wave growth. We also detect fundamental Pc4‐5 waves near the plasmapause on the nightside in the drift resonance with 100–150 keV ions. Simulation results suggest that the plasmapause has an effect to sustain the excitation of Pc4‐5 ULF wave through the drift resonance.

Solving nonconvex energy minimization problems in martensitic phase transitions with a mesh-free deep learning approach

In this paper, we propose a novel mesh-free method for solving nonconvex energy minimization problems for martensitic phase transitions and twinning in crystals using the deep learning approach. These problems pose significant challenges to analysis and computation because they involve multiwell gradient energies with large numbers of local minima, each involving a topologically complex microstructure of free boundaries with gradient jumps. We use the Deep Ritz method, which represents candidates for minimizers using parameter-dependent deep neural networks, and minimize the energy with respect to network parameters. The key feature of our method is a newly proposed activation function called SmReLU, which captures the structure of minimizers where traditional activation functions fail. Our mesh-free approach allows for the approximation of free boundaries, essential to this problem, without any special treatment, making it extremely simple to implement. We demonstrate the success of our method through numerous numerical computations.

Janus membranes with opposite wettability prompting the synchronous synthesis and separation of hydrophobic ionic liquids

Traditional production of ionic liquids (ILs) includes isolated processes of synthesis followed by extraction purification with organic solvents. A remained challenge is to produce these green solvents by a simultaneous synthesis and separation procedure disusing volatile organic solvents. Herein, we describe a framework for the synchronous synthesis and separation of hydrophobic ILs based on an environmentally benign membrane reactor system. A Janus hollow fiber membrane reactor (JHFMR) with a thin and charged inner surface (IL-phobic) and an IL-philic outer surface is prepared by mussel-inspired co-deposition technique. The hydrophilic lumen surface supplies a reaction zone for anion metathesis. The inner surface charge destabilizes the emulsified target ILs dispersed in water. The deemulsified ILs actively pass through the JHFMR from IL-phobic side to IL-philic side driven by the gradient of surface energy. Multiple JHFMRs are ultimately assembled to prepare a JHFMR module for achieving a continuous and large-scale production of hydrophobic ILs in a cross-flow mode. The final ILs yield under a low reactant concentration (l.0 mol/L) is enhanced to reach 96% after 30 h by doubling the packing density of module. The residual water content in IL products is below 1.0 wt%. Other ion impurity is negligible (Li+ < 10 ppm, and Br- is below the detectable limit). Such enormously low impurity level is attributable to the synchronous separation of ILs once they are synthesized within the JHFMR module. Moreover, the module maintains a stable performance after repeated cycles. The proposed all-in-one strategy has a potential for continuous preparation of hydrophobic ILs at a large scale, with high yield and low impurity under “greener” operating conditions, e.g., at room temperature and avoidance of using volatile organic solvents.

Engineered cellulose nanofibers membranes with oppositely charge characteristics for high-performance salinity gradient power generation by reverse electrodialysis

Reverse electrodialysis (RED) using nanofluidic ion-selective membrane may convert the salinity difference between seawater and river water into electricity. However, heterogeneous modification reactions of cellulose commonly leads to the inhomogeneous distribution of surface charges, thereby hampering the improvement of cellulose-based nanofluidic membranes for energy conversion. Herein, RED devices based on cellulose nanofibers (CNF) membranes with opposite charge characteristics were developed for the generation of salinity gradient power. Anion-CNF membrane (A-CNF) with varying negative charge densities was synthesized using 2,2,6,6-Tetramethylpiperidine 1-oxy radical (TEMPO) oxidation modification, whereas cation-CNF membrane (C-CNF) was prepared through etherification. By mixing artificial seawater and river water, the output power density of CNF RED device is up to 2.87 W m−2. The output voltage of 30 RED units connected in series may reach up to 3.11 V, which can be used to directly power tiny electronic devices viz. LED lamp, calculator, etc. The results of this work provide a feasible possibility for widespread application of ion exchange membranes for salinity gradient energy harvesting.

Mechanisms for Charge Selectivity on Semiconducting Photocatalyst Particles

Overall-water splitting on photocatalysts provides a direct-unassisted path in the conversion of solar energy to chemical energy. Optoelectronic properties (absorbing incident light with long excited state lifetimes) and carrier selective contacts (transporting and transferring the desired electronic carrier to the targeted redox active species) are two key parameters that govern photocatalyst behavior. However, the advantageous small geometry of the highest achieving photocatalysts makes measurement of their carrier selective contacts difficult. Additionally, several mechanisms that enable high energy-conversion efficiencies and large gradients in free energy manifest only at the nanoscale at individual nanoparticle sites. SrTiO3 has been extensively studied and shown to split water with high quantum yields when decorated with HER and OER catalysts. SrTiO3 is used, in this work, as a model system to study mechanisms for charge selectivity on overall-water splitting photocatalyst particles.Here, we use three sample geometries to measure local, facet, and catalyst-dependent, electrochemical driving forces and their synergistic enhancement of carrier selectivity, (single crystal planar (b), single crystal co-facet exposed planar (a), facetted nanoparticles (c) loaded with OER and HER catalysts [{Pt/CrO3, Rh/CrO3} and CoOOH respectively]). We use ex-situ conductive atomic force microscopy to individually interrogate the electrical properties of nano-scale catalyst/semiconductor junctions decorated on facet-engineered surfaces of SrTiO3. Supporting experiments of SECM and Operando AP-XPS will be used to measure the charge carrier selectivity when an electrolyte is present and connect the ex-situ characterization observations to operando conditions. In summary, these findings demonstrate the underlying mechanisms and the degree that they play, enabling directed research of photocatalyst systems under the two dominant engineering conditions, high optoelectronic properties and charge selective contacts. Figure 1

In Situ Observation of Domain Wall Lateral Creeping in a Ferroelectric Capacitor

AbstractAs a promising candidate for next‐generation nonvolatile memory devices, ferroelectric oxide films exhibit many emergent phenomena with functional applications, making understanding polarization switching and domain evolution behaviors of fundamental importance. However, tracking domain wall motion in ferroelectric oxide films with high spatial resolution remains challenging. Here, an in situ biasing approach for direct atomic‐scale observations of domain nucleation and sideways motion is presented. By accurately controlling the applied electric field, the lateral translational speed of the domain wall can decrease to less than 2.2 Å s−1, which is observable with atomic resolution STEM imaging. In situ observations on a capacitor structured PbZr0.1Ti0.9O3/La0.7Sr0.3MnO3 heterojunction demonstrate the unique creeping behavior of a domain wall under a critical electric field, with the atomic structure of the creeping domain wall revealed. Moreover, the evolution of the metastable domain wall forms an elongated morphology, which contains a large proportion of charged segments. Phase‐field simulations unveil the competition between gradient, elastic, and electrostatic energies that decide this unique domain wall creeping and morphology variation. This work paves the way toward a complete fundamental understanding of domain wall physics and potential modulations of domain wall properties in real devices.

Textured surfaces for oil droplet transport

Droplet-based microfluidic systems bring the advantage of handling samples in discrete forms and these systems can be built as a surface-based platform, eliminating the need of a carrier fluid. Droplet transport on surfaces can be achieved by creating local energy gradients by using electrowetting, thermocapillary forces, chemical gradients and surface texture. These methods are developed for aqueous droplets; while controlled transportation of oil droplets remains as a challenge due to their low surface tension. One of the major challenges in achieving controlled oil droplet manipulation is to obtain oil repellent -oleophobic- surfaces. In this work, pillar arrays with mushroom shaped profiles were designed, fabricated, and tested to study oil wetting on textured surfaces. Contact angles higher than 170° were achieved for hexadecane droplets in Fakir state. Based on these findings, surface texture ratchet tracks that are composed of an array of arc shaped pillars were built to generate local energy gradients to manipulate oil droplets in a continuous fashion. Motion of hexadecane droplets at a speed of 7 mm/s was achieved. The results of this study are crucial for applications of oil droplet transport such as in biochemistry, smart surface development, wearable device design as well as microsystem packaging.

Extending Density Phase-Field Simulations to Dynamic Regimes

Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers.