Total Energy Dissipation Research Articles

Indentation fracture of 4H-SiC single crystal

Understanding the deformation and fracture behavior of single crystal silicon carbide (SiC) under a single particle is of scientific and practical importance for the micromachining of single crystal SiC. In this work, we investigate the indentation fracture of a 4H-SiC single crystal wafer with the indentation direction perpendicular to (0001) plane, using Berkovich, Vickers, and Knoop indenters. All the indentations create radial cracks for the normal loads used in this work. Both the Vickers and Knoop hardness tests produce lateral cracks. The fracture toughness calculated from the Vickers hardness tests is smaller than the ones calculated from the Knoop hardness tests and the Berkovich indentations under large indentation loads. The fracture toughness of 4H-SiC single crystal decreases with the increase of the indentation load under small indentation loads for the Berkovich indentations, revealing the phenomenon of surface hardening. The surface energy calculated from the radial cracks is comparable to the results reported in the literature. We establish an analytical expression of the total energy dissipation of a single indentation cycle, including the contribution of indentation-induced cracking, which offers an approach to calculate the ratio of the energy dissipation due to cracking to the energy dissipation due to plastic deformation and determine the dominant deformation process controlling the indentation deformation. The analysis of the energy dissipation for the indentations of the 4H-SiC single crystal by the Berkovich indenter reveals that the energy dissipation from the indentation-induced cracking is significantly larger than (more than eight times) that from plastic deformation for the indentation loads larger than 75 mN.

Effects of Prestressing Magnitude and Position on Seismic Performance of Unbonded Prestressed Concrete Beams

To study the effects of the jacking stress level, height and strength ratio of the prestress tendons (λ) on the seismic performance of unbonded prestressed concrete (UPC) beams, six UPC beams and one reinforced concrete (RC) beam were tested under cyclic loads. The hysteretic characteristics, skeleton curves, ductility properties, energy dissipation capacity, strain distribution of reinforcement and self-centering capability of the specimens were studied and discussed. Numerical parameter analysis was also carried out by using OpenSees. The results indicate that three failure modes of UPC beams under cyclic loading were observed, namely the tension-failure mode involving a broken rebar, the compression-failure mode involving concrete crushing and the balanced failure. By considering the influence of the prestress position and magnitude, the modified reinforcing index ω was proposed to determine the failure mode. The ω is suggested to be less than 0.3 to ensure sufficient ductility. The effective stress level is linearly and positively related to the stiffness from cracking to yield Kcr and the ultimate bearing capacity of the UPC beam under cyclic loading. The stiffness of the UPC beam is slightly larger than that of the RC beam before yielding, and significantly greater than that of the RC beam after yielding. Due to the large strength reserve after yielding, the integrated seismic performance of the UPC beam is similar to that of the RC beam. When the λ was unchanged, the increase in the relative height of the prestressed tendons αh is beneficial for the overall performance factor F, ductility and crack control. The stiffness degradation performance depends on the λ but is independent of the αh. The total energy dissipation of the non-tensioned UPC specimen was 59% higher than that of the RC beam. The cumulative total energy dissipation of the tensioned UPC specimen was only 13% lower than that of the RC beam with the same number of cycles, indicating that the UPC specimen had a considerable energy dissipation capacity.

A Hybrid Heuristic Model for Duty Cycle Framework Optimization

This paper proposes a hybrid metaheuristic approach to optimize a duty cycle framework based on Seagull and Mayfly Optimization (HSMO-DC) Algorithm. This approach becomes crucial as current clustering protocols are unable to efficiently tune the clustering parameters in accordance to the diversification of varying WSNs. The proposed HSMO-DC primarily has two parts, where the first part takes care of the online cluster head selection and network communication using the seagull algorithm while the second part performs parameter optimization using the mayfly algorithm. The seagull is aimed at improving the energy distribution in the network through an effective bandwidth allocation procedure while reducing the total energy dissipation. Comparatively, with other clustering protocols, our proposed methods reveal an enhanced network lifetime with an improved network throughput and adaptability based on selected standard metric of performance measurement.

Damage analysis of a pseudoclassic reinforced concrete frame structure under the action of the Ms 6.8 Luding earthquake in China

Reinforced concrete (RC) moment-resistant frame structures are very commonly used worldwide. However, previous earthquakes have revealed the occurrence of strong beam–weak column (SBWC) failure, causing heavy human casualties and economic losses. This study analyzed the SBWC failure mechanism in RC frame structures with the pseudoclassic construction named "Que Ti" near the top of a slope topography, based on the author's recent investigation of the Ms 6.8 Luding earthquake in China. Eight refined finite element models (FEMs) were developed to simulate and analyze the influence of slope topography, pseudoclassic construction, and some structural characteristics on structural damage during an earthquake. Furthermore, discussions on using column-to-beam flexural strength ratios (CBFSRs) to mitigate SBWC failure are presented. The results demonstrated the proposed FEMs effectively simulated the performance of the pseudoclassic structure, especially the SBWC failure mode, as validated by their consistency with the observed structural damage during the earthquake. Moreover, it revealed that structures closer to the slope top experienced amplified ground motions during earthquakes, resulting in more severe damage. In addition, the Que Ti and infill walls increased the vulnerability to column damage and maximum requirement for the column shear force. Finally, to achieve the design objective of a strong column–weak beam (SCWB), the CBFSR should be at least increased to 1.8 for this pseudoclassic RC frame. This ensures a probability of the SBWC failure mode of less than 17% (meet less than 20% of recommendations) and proportion of the beam plastic energy dissipation exceeding 80% of the total plastic energy dissipation. The findings of this study are significant for enhancing seismic design and preventing earthquake disasters for the pseudoclassic structure.

Novel energy efficient RND inverter using quantum dot cellular automata in nanotechnology

Quantum-Dot Cellular Automata (QCA) is a promising technology for designing high-performance and efficient logic circuits, surpassing traditional Complementary Metal Oxide Semiconductor approaches. In today’s digital era, the demand for digital circuits with high speed, device density, and energy efficiency is paramount. This paper focuses on the innovative Rotated Normal Cells with Displacement (RND) inverter model, employing normal and rotated cells with a 10 nm displacement through a cell interactive method. Digital circuits designed using the RND inverter exhibit superior performance compared to existing designs. The proposed RND inverter gate utilizes only four QCA cells, occupying a total area of 4525.55 nm2. With a total energy dissipation of 0.508 meV and an average energy dissipation per cycle of 0.0462 meV, it achieves a polarization of 9.77. The novel RND inverter demonstrates a 44% improvement in cell area and a 63% reduction in total area compared to current designs, offering enhanced energy efficiency with 0.26 improved polarization. The RND inverter and the digital circuits facilitate finding applications in efficiently constructing various components within Quantum Computers. Beyond quantum computing, the RND inverter proves applicable in designing Nano-sized electronic gadgets and temperature-controlled circuits, showcasing its versatility across diverse technological applications.

New Insights Optimize Landing Strategies to Reduce Lower Limb Injury Risk.

Single-leg landing (SL) is often associated with a high injury risk, especially anterior cruciate ligament (ACL) injuries and lateral ankle sprain. This work investigates the relationship between ankle motion patterns (ankle initial contact angle [AICA] and ankle range of motion [AROM]) and the lower limb injury risk during SL, and proposes an optimized landing strategy that can reduce the injury risk. To more realistically revert and simulate the ACL injury mechanics, we developed a knee musculoskeletal model that reverts the ACL ligament to a nonlinear short-term viscoelastic mechanical mechanism (strain rate-dependent) generated by the dense connective tissue as a function of strain. Sixty healthy male subjects were recruited to collect biomechanics data during SL. The correlation analysis was conducted to explore the relationship between AICA, AROM, and peak vertical ground reaction force (PVGRF), joint total energy dissipation (TED), peak ankle knee hip sagittal moment, peak ankle inversion angle (PAIA), and peak ACL force (PAF). AICA exhibits a negative correlation with PVGRF (r = -0.591) and PAF (r = -0.554), and a positive correlation with TED (r = 0.490) and PAIA (r = 0.502). AROM exhibits a positive correlation with TED (r = 0.687) and PAIA (r = 0.600). The results suggested that the appropriate increases in AICA (30° to 40°) and AROM (50° to 70°) may reduce the lower limb injury risk. This study has the potential to offer novel perspectives on the optimized application of landing strategies, thus giving the crucial theoretical basis for decreasing injury risk.

Study of Phase Imaging Contrast Optimization in Tapping Mode Atomic Force Microscopy

In tapping mode atomic force microscopy (TM‐AFM), the phase image can reveal more about the physicochemical properties of the sample surface than the topography image, making it widely utilized in fields such as materials science and life sciences. However, obtaining high phase contrast in phase images during experiments is challenging, thus studying the phase imaging theory of TM‐AFM and optimizing phase contrast methods hold significant importance. This paper derives a theoretical expression for phase contrast based on phase theory, discovering that phase contrast is directly related to the frequency ratio and background dissipation quality factor. Through theoretical, experimental, and simulation approaches, optimization methods for phase contrast were proposed from the perspectives of frequency ratio and background dissipation quality factor as follows: (1) By fitting experimental results with the theoretical expression for phase contrast, the optimal frequency ratio for scanning can be determined, and imaging with this optimal ratio can enhance phase contrast and (2) reducing the width ratio between the free and fixed ends of the probe can decrease background dissipation, increase the proportion of core dissipation in the total energy dissipation of the probe, and thereby improve phase imaging contrast. These findings are significant in guiding TM‐AFM phase scanning experiments and optimizing phase imaging contrast.

Experimental study on hysteretic performance of self-centring energy dissipation beam-to-column connections equipped with SMA plates

Shape memory alloys (SMAs) exhibit excellent superelasticity. Using SMA members together with other energy dissipation members can help balance the self-centring and energy dissipation capacities of structures to achieve a better seismic performance. A novel type of self-centring energy dissipation beam-to-column connection equipped with SMA plate was proposed. The quasi-static tests were conducted and the hysteretic performance of the connections was evaluated. The results show that the bending strength and stiffness of the specimens equipped with a two-layer SMA connecting plate were larger than those of the specimens equipped with a one-layer SMA plate. The connections showed a good self-centring performance, and the maximum residual drift angle was only 0.35% when unloading from 4% drift angle. The SMA-Q160/ALA connection could recover 79.2% of the loading angle at most. Moreover, a SMA-Q160/ALA parallel system configuration could significantly improve the energy dissipation capacity of beam-to-column connections. The total energy dissipation and equivalent viscous damping coefficient were larger than those of the connections equipped with only SMA plate.

Structure-function relationships in the nasal cavity of Arctic and subtropical seals

The heating and moistening of inhaled air, and the cooling and moisture removal from exhaled air, are crucial for the survival of animals under severe environmental conditions. Arctic mammals have evolved specific adaptive mechanisms to retain warmth and water and restrict heat loss during breathing. Here, the role of the porous turbinates of the nasal cavities of Arctic and subtropical seals is studied with this in mind. Mass and energy balance equations are used to compute the time-dependent temperature and water vapor profiles along the nasal passage. A quasi-1D model based on computed tomography images of seal nasal cavities is used in numerical simulations. Measured cross-sectional areas of the air channel and the perimeters of the computed tomography slices along the nasal cavities of the two seal species are used. The model includes coupled heat and vapor transfer at the air-mucus interface and heat transfer at the interfaces between the tissues and blood vessels. The model, which assumes constant blood flow to the nose, can be used to predict the temperature of the exhaled air as a function of ambient temperature. The energy dissipation (entropy production) in the nasal passages was used to measure the relative importance of structural parameters for heat and water recovery. We found that an increase in perimeter led to significant decreases in the total energy dissipation. This is explained by improved conditions for heat and water transfer with a larger complexity of turbinates. Owing to differences in their nasal cavity morphology, the Arctic seal is expected to be advantaged in these respects relative to the subtropical seal.

FED evaluation in a small double-suction reversible pump turbine considering sediment erosion

Double-suction pump-turbines are a special type of reversible pump-turbine which serves the pumped storage hydro power plant. Enhancing the energy conversion efficiency of the power station can be effectively achieved by reducing the internal Flow Energy Dissipation (FED) within the pump-turbine. The key to addressing this challenge lies in the identification of high FED regions and conducting visualized analyses. In this study, computational fluid dynamics (CFD), thermodynamic calculation methods and the Finnie erosion model are combined to perform two-phase flow numerical simulations of a specific double-suction pump-turbine model under both pump and turbine operating modes. We analyzed the FED in different regions off wall. The energy loss distribution is provided within these five regions for the volute casing, suction chamber, and impeller separately, and conducted an analysis of component wear. The research findings revealed that, in the pump mode, FED primarily concentrates within the volute casing, while in the turbine mode, it is concentrated within the suction chamber, with both regions accounting for over 70 % of the total energy dissipation. The proportion of internal FED in five regions at varying distances from the wall for each component showed significant disparities under different operating conditions, closely related to the internal flow characteristics of the components. In pump mode, wear primarily occurs in the volute casing, while the wear in the suction chamber and impeller can be considered negligible. In turbine mode, each component experiences some level of wear. This provides a foundation for reducing flow energy losses and preventing sediment erosion.

On the post-impact fatigue behavior and theoretical life prediction of CF/PEEK-titanium hybrid laminates using an energy dissipation approach

This paper aims to illustrate the effect of the impact damage on fatigue behavior of CF/PEEK-titanium hybrid laminates. To achieve this end, a fatigue life model was proposed to predict the S–N curves of the laminates at various initial impact energy levels and stress ratios based on the energy dissipation approach. The energy dissipation behavior of the laminates during fatigue loading under different experimental conditions was analyzed through a large amount of post-impact fatigue tests, and the correlation between the initial impact damage and the total fatigue dissipation energy was determined. The full-field axial strain distribution of the titanium layer on the impacted side of the laminate was characterized in terms of initial impact energy level and maximum stress using digital image correlation, and then the post-impact fatigue failure mechanism of CF/PEEK-Ti hybrid laminates was summarized. Finally, the validity of the proposed model was verified by fatigue tests under other conditions of stress ratio and impact energy level. It is worth mentioning that the proposed model is also applicable to other types of FMLs, and can accurately predict the residual fatigue life of laminates after impact with only one set of S–N curve data.

Full-lung simulations of mechanically ventilated lungs incorporating recruitment/derecruitment dynamics.

This study developed and investigated a comprehensive multiscale computational model of a mechanically ventilated ARDS lung to elucidate the underlying mechanisms contributing to the development or prevention of VILI. This model is built upon a healthy lung model that incorporates realistic airway and alveolar geometry, tissue distensibility, and surfactant dynamics. Key features of the ARDS model include recruitment and derecruitment (RD) dynamics, alveolar tissue viscoelasticity, and surfactant deficiency. This model successfully reproduces realistic pressure-volume (PV) behavior, dynamic surface tension, and time-dependent descriptions of RD events as a function of the ventilation scenario. Simulations of Time-Controlled Adaptive Ventilation (TCAV) modes, with short and long durations of exhalation (T Low - and T Low +, respectively), reveal a higher incidence of RD for T Low + despite reduced surface tensions due to interfacial compression. This finding aligns with experimental evidence emphasizing the critical role of timing in protective ventilation strategies. Quantitative analysis of energy dissipation indicates that while alveolar recruitment contributes only a small fraction of total energy dissipation, its spatial concentration and brief duration may significantly contribute to VILI progression due to its focal nature and higher intensity. Leveraging the computational framework, the model may be extended to facilitate the development of personalized protective ventilation strategies to enhance patient outcomes. As such, this computational modeling approach offers valuable insights into the complex dynamics of VILI that may guide the optimization of ventilation strategies in ARDS management.

Trajectories and Forces in Four-Electrode Chambers Operated in Object-Shift, Dielectrophoresis and Field-Cage Modes-Considerations from the System's Point of View.

In two previous papers, we calculated the dielectrophoresis (DEP) force and corresponding trajectories of high- and low-conductance 200-µm 2D spheres in a square 1 × 1-mm chamber with plane-versus-pointed, plane-versus-plane and pointed-versus-pointed electrode configurations by applying the law of maximum entropy production (LMEP) to the system. Here, we complete these considerations for configurations with four-pointed electrodes centered on the chamber edges. The four electrodes were operated in either object-shift mode (two adjacent electrodes opposite the other two adjacent electrodes), DEP mode (one electrode versus the other three electrodes), or field-cage mode (two electrodes on opposite edges versus the two electrodes on the other two opposite edges). As in previous work, we have assumed DC properties for the object and the external media for simplicity. Nevertheless, every possible polarization ratio of the two media can be modeled this way. The trajectories of the spherical centers and the corresponding DEP forces were calculated from the gradients of the system's total energy dissipation, described by numerically-derived conductance fields. In each of the three drive modes, very high attractive and repulsive forces were found in front of pointed electrodes for the high and low-conductance spheres, respectively. The conductance fields predict bifurcation points, watersheds, and trajectories with multiple endpoints. The high and low-conductance spheres usually follow similar trajectories, albeit with reversed orientations. In DEP drive mode, the four-point electrode chamber provides a similar area for DEP measurements as the classical plane-versus-pointed electrode chamber.

Rapid and scalable synthesis of novel carboxylated aramid nanofibers for simultaneously improving the strength and toughness of carbon fiber/epoxy laminates

Carbon fiber reinforced composites (CFRCs) are widely used in the aviation, aerospace and automotive industries. The modification of CFRCs with nanomaterials has attracted extensive research interests in recent years. Herein, we report the preparation of novel carboxylated aramid nanofibers (cANFs) by polymerization induced self-assembly, i.e. polycondensation of para-phenylenediamine with terephthaloyl chloride in the presence of a polyamide acid as both a dispersant and surface modifier, for the modification of epoxy resin and CFRCs. cANFs effectively improve the mechanical properties of epoxy resin, and after being sprayed onto CF fabrics, greatly improve the mechanical properties of CFRCs. With the addition of only 0.42 mg/cm2 of cANFs on each CF sheets, storage modulus, flexural strength, flexural modulus and total energy dissipation are enhanced by 27 %, 51 %, 29 % and 67 %, respectively; interlaminar shear strength (ILSS) and Mode II interlayer fracture toughness (GIIC) are improved by 24 % and 74 %, respectively. cANFs can be comparable or even superior to most previously reported carbon nanomaterials in improving flexural strength and ILSS; and exceed most previously reported electrospun nanofibrous mats in increasing GIIC. This study provides a new method for the rapid synthesis of functionalized ANFs to simultaneously increase the flexural properties and interlayer properties of CFRCs.

The effect of surface roughness on the viscoelastic energy dissipation in a particle–wall collision

The particle collision on a wall with roughness is common in nature and industries, but not well understood yet. The presence of surface roughness greatly increases the complexity of local contact and makes it difficult to predict the energy dissipation by analytical models. In this work, we investigate the energy dissipation in a dynamic particle–wall collision with regular hemisphere roughness. The finite element method (FEM) with the standard linear solid model is used to solve the problem of non-ideal geometry, and extract the law of energy dissipation due to viscoelasticity. The results show that with the existence of surface roughness, the total viscoelastic dissipation is lower than that for a smooth surface, showing a higher restitution coefficient compared to the smooth surface. Based on the maximum number of asperities that particle contacts, the dynamic collisions can be categorized as the single-contact mode and multiple-contact mode. The variation of the total energy dissipation shows opposite trends with the roughness height in the two different modes. The collision time is recognized as the key to predict the total energy dissipation. Based on FEM simulation results, a piecewise correlation is established to estimate the Hertzian collision time with regular roughness. Finally, a correlation is proposed for the total energy dissipation in a viscoelastic particle–wall collision with regular roughness, which only takes the dimensionless relaxation time as the parameter. Covering different roughness heights, particle sizes, densities, relaxation times, and Young’s modulus, all the data are well correlated with the predicted curve.

Morphometric properties, scaling laws and hydrologic response of the Greater Paris combined sewer system

AbstractMorphometric properties of channel networks are useful tools to classify catchments and calculate their hydrological response. Scaling laws have been established for Optimal Channel Networks (OCNs), which are defined based on a generative geomorphological mechanism of minimizing the total energy dissipation. However, sewer networks obey engineering efficiency rules and are conceived based on local optimizations, both in time and space, for minimal costs. Not all the scaling laws have been verified for artificial sewer networks found in urban areas. This raises questions regarding the applicability of OCN scaling laws to sewer networks and their potential impact on the shape of the Geomorphological Instantaneous Unit Hydrograph (GIUH). Hence, this work aims to study the morphometric properties of the Greater Paris combined sewer system through a case study on twelve nested subcatchments. A two‐step methodology is used. First, the morphometric properties are analysed using the reference Horton‐Strahler, Rodríguez‐Iturbe and Moussa‐Bocquillon scaling laws. The results show that Horton‐Strahler's laws of bifurcation are verified while the length and area laws are not always verified. Rodriguez‐Iturbe and Moussa‐Bocquillon laws are verified with slightly different values of the descriptors in comparison to OCNs. Second, these morphometric properties are used to calculate four GIUHs: the reference Width Function (GWF), the Nash unit hydrograph (GN) using Horton‐Strahler ratios, the Nash Unit Hydrograph equivalent (GNe) using Moussa‐Bocquillon descriptors, and the Hayami function (GH) solution of the diffusive wave equation. We identified four catchments for which the scaling laws are verified and therefore all GIUHs are similar while for four other catchments the scaling laws are not verified and strongly impact the GIUHs. These morphometric descriptors and the GIUHs can be considered as ‘hydrological signatures’ of Combined Sewer Systems (CSSs) and are useful for the comparison and classification of hydrological responses.

Maximum spreading of an impacting drop

The maximum diameter of a drop impacting on a flat solid surface is studied theoretically assuming axi-symmetric spreading without splashing. The energy balance between the initial state of the drop (sphere diameter d0) and that a maximum spread (contact diameter dm) is closed by two novel concepts. For the gas-liquid surface area, an approximate spherical cap model is proposed. Energy loss by viscous dissipation is related to the total energy dissipation when the drop has come to rest. The fractional dissipation upon maximum spread is modelled as a function of an impact parameter (P) that combines the power laws of the capillary and viscous regimes depending on a regime discrimination parameter (A). Exponents of the Weber (We) and Reynolds (Re) numbers in P=WeRe−2/5 are determined by asymptotic analysis. The parameter A is determined from experimental data as a function of the advancing contact angle (θa). In this way, an explicit model for the maximum spread factor (βm=dm/d0) is proposed which includes the scaling laws βm∼We1/2, βm∼We1/4 and βm∼Re1/5 and is in good agreement with experimental data for wide ranges of We, Re and θa.

Feasibility of utilising waste tyre steel fibres to develop sustainable engineered cementitious composites: Engineering properties, impact resistance and environmental assessment

This study investigates the feasibility of developing sustainable engineered cementitious composite (ECC) with polyvinyl alcohol fibre (PVAF) and recycled tyre steel fibre (RTSF) to reduce the total cost of construction materials and ease the environmental pressure for disposing of waste tyres, putting an emphasis on the engineering properties, impact resistance and environmental assessment. Experimental results reveal that partially replacing PVAF with RTSF can reduce the loss in fluidity and promote flexural performance, while the fibre bridging stress of ECC can reach up to 4.41 MPa because of the enhanced fibre bridging effect. The dynamic compressive properties of ECC present a typical strain rate effect regardless of the fibre content, and the replacement of 0.25 vol% RTSF would cause a further 5.03%–25.55% increase in total dissipation energy within the strain rates of 58.2–124.5 s−1, relative to ECC reinforced by 2.0 vol% PVAF. The synergetic effects of hybrid fibres on dynamic compressive properties of ECC can be explained by the bridging and pull-out effects of PVAF at lower strain rates, as well as the enhanced fibre-to-matrix bonding of hydrophilic RTSF at relatively higher strain rates. Upcycling of waste steel fibres in ECC holds promise as a cost-effective and eco-friendly solution for defence engineering constructions.

A fast fatigue life estimation method for concrete based on the energy dissipation approach

This study proposed a concrete fatigue life prediction method based on energy dissipation analysis. The fatigue life is estimated by dividing the total critical energy dissipation by the average energy dissipation per cycle. Based on a unified concrete damage model that can be applied to both monotonic and fatigue loading conditions, the total critical energy dissipation value under fatigue loading can be estimated by the stress-strain curve under monotonic loading. The average energy dissipation per cycle is obtained by calculating numerical samples with different strengths. Several numerical examples show that the proposed prediction model can rapidly estimate fatigue life under uniaxial loading with high efficiency and excellent precision.

Backscatter in energetically-constrained Leith parameterizations

This paper combines two strains in the literature on subgrid-scale parameterizations for eddying ocean models to develop six new parameterizations and test them in an idealized quasigeostrophic model. The first strain develops nonlinear, Smagorinsky-like Leith scalings for the viscous coefficient based on reasoning about the turbulent forward enstrophy cascade of geophysical turbulence. The second introduces backscatter whose amplitude is scaled to re-inject a portion of the energy dissipated by other parameterizations. In the new parameterizations developed here the backscatter and viscous coefficients depend on each other and are set to simultaneously absorb the forward enstrophy (or potential enstrophy) cascade and backscatter a portion of the dissipated energy. The addition of backscatter to Leith-scaled nonlinear viscosity improves the simulations at resolutions from 4 km to 24 km by increasing the total kinetic energy and by reducing the fraction of the total energy dissipation rate associated with the net effect of viscosity and backscatter. Versions that use biharmonic viscosity to absorb the enstrophy cascade perform better than versions using a harmonic viscosity, and purely viscous closures perform better than closures that dissipate both kinetic and potential energy. Stochastic and deterministic backscatter schemes are developed, and though similar, the deterministic schemes perform slightly better.