Abstract: To provide a new technique for efficiently recovering microplastics from water to be treated, in which problems of conventional techniques such as large energy consumption are solved. A method for recovering microplastics from water to be treated containing the microplastics, the method comprising a step of allowing algae having microplastic adsorption and recovery ability to be present in the water to be treated, in which the algae are algae that secrete a sticky substance, and an amount of a sticky substance secreted by the algae is such that a volume of a sticky substance secreted to an outside of cells is 0.25 times or more and 100 times or less compared to a cell volume.

Abstract: A system for reducing contaminants in body of water is shown and described. The system has a first land mass located within a body of water. A sediment trap, located on the floor of the body of water, is configured to collect sediment. Enclosed within the first land mass is a tussock mass area, surrounding a central area, and configured for collecting sediment and building a second land mass. The central area of the system is configured for removing contaminants from sediment. Sediment is moved from the sediment trap to the central area by a first ingress conduit and a pumping system. Filtered water migrates from the central area to outside the first land mass via an egress conduit; contaminated sediment is sequestered in the central area enclosed by the tussock mass area.

Abstract: The present application relates to the technical field of water environment governance, and particularly discloses a method for accurate positioning and in-situ treatment of pollutants at a sediment-water interface. In the method, high-throughput sequencing technology and pollutant source apportionment technology are firstly used to perform accurate positioning on the sediment to be controlled, and then electrodialysis-vacuum negative pressure dewatering technology is used to perform in-situ dewatering treatment on the sediment to be controlled, thereby realizing accurate governance with the minimum desilting amount. In the present application, in further cooperation with the application of microbial reagents, the microbial flora environment of the sediment-water interface is regulated, thereby increasing the dewatering speed of the sediment.

Abstract: A system (20, 70) for water treatment includes a plurality of containers (22, 24, 26, 80) which are configured to be stacked one on another for shipment and to deployed in a row at different, respective heights at a water treatment site. Each container includes an inlet (37, 86) at a first side of the container and an outlet (88) at a second side of the container, opposite the first side. The containers are filled with substrates (36, 38, 40) configured for planting of aquatic plants (60) therein and including at least different first and second substrates for filling the first and second containers, respectively. Piping includes at least an inlet pipe (34) for connection to the inlet of a first container, a transfer pipe (64, 66) for connection between the outlet of the first container and the inlet of a second container, and an outlet pipe (41) for connection to the outlet of the second container.

Abstract: A method of using algae to remove a contaminant or pollutant from a first fluid is provided. The method can include providing a growing apparatus having a first reservoir containing the first fluid and a second reservoir containing a second fluid, and growing the algae using the growing apparatus. The method can further include exposing the algae to the first fluid within the first reservoir where the algae uptakes the contaminant or pollutant from the first fluid, and exposing the algae via a belt to the second fluid in the second reservoir where the algae is stimulated to release the contaminant or pollutant. Exposing the algae to the first fluid within the first reservoir or the second fluid may change a growth rate of the algae.

Abstract: Methods are provided for inhibiting cyanobacteria. The methods include treating a substance contaminated with cyanobacteria with a composition. The composition includes Citrus medica Linn. or an extract of the same.

Abstract: The embodiments of the present technology relate in general to an improved bioretention system for stormwater treatment through volume control and various filtration processes in a horizontal flow media bed. In particular, the disclosed bioretention system transfers water through the media bed horizontally and notably has two sided void area for influent runoff to pond and build up adjacent to the media bed where water is pre-treated, sediments settle on the floor area and water flows into the media bed via its vertical surface.

Abstract: The present invention discloses a tower-shape integrated ecological purification device for domestic sewage in a small town. The device includes a water storage and filter pond, a medium reverse osmosis pond, an amphibious biological reaction system, and an aquatic biological reaction system. The amphibious biological reaction system and the aquatic biological reaction system are alternately connected from the top down. The amphibious biological reaction system and the aquatic biological reaction system form an alternating dry and wet, oxidation-reduction compound environment. Plant absorption, biological substrate transformation, aeration, and strengthening medium adsorption are combined to form a multi-stage plant-microbe-animal integrated ecological purification treatment process/device. The present invention achieves the efficient purification and acceptable discharge of domestic sewage in small towns.

Abstract: The invention relates to an electrolytic cell equipped with microelectrodes for the generation of un-separated products and the method for obtaining it. The cell and the microelectrodes of the present invention are obtained using a technology for the production of microelectromechanical systems (MEMS). The anodic and cathodic microelectrodes have an electrocatalytic coating and are mutually intercalated at an interelectrodic gap lower than 300 micrometres.

Abstract: The present invention relates to a system or method for the remediation of wastewater with a treatment media in tandem with an electrocoagulation system. The system and method also include cleaning elements for cleaning distribution lines within the system and for cleaning the electrocoagulation system.

Abstract: A process of removing contaminants and concentrating wastewater includes delivering wastewater from a source of wastewater to a hydrogen sulfide removal device, mixing an oxidant with the filtered wastewater in the hydrogen sulfide removal device to produce a hydrogen sulfide lean effluent, delivering the hydrogen sulfide lean effluent to a direct contact concentrator, and evaporating a portion of the hydrogen lean effluent in the direct contact evaporator to produce a slurry and an exhaust gas.

Abstract: A process for treating domestic wastewater may include directing wastewater into a tank containing a membrane filter and mixed liquor. The process may include recirculating wastewater and mixed liquor from a top end of the tank into a bottom end of the tank via a recirculation conduit. The process may include introducing a flow of wastewater and mixed liquor from the recirculation conduit into an aeration device and drawing ambient air into the aeration device using the flow of wastewater and mixed liquor from the recirculation conduit. The process may also include drawing wastewater and mixed liquor proximately surrounding the aeration device into the aeration device using the flow of wastewater and mixed liquor from the recirculation conduit. The process may include aerating a mixture of wastewater and mixed liquor with the ambient air below the membrane filter.

Abstract: A process for constructing a soil-based rhizosphere flow-through system to break down contaminants in contaminated water. The process includes the steps of: providing plants planted in soil in a test bioreactor, the plants providing a rhizosphere; exposing the rhizosphere to the contaminated water; extracting microorganisms from the rhizosphere following their exposure to the contaminated water; preparing a microbial suspension from the extract; subjecting the microbial suspension to growth conditions to increase the concentration of the microorganisms, thereby preparing a soil conditioner; adding the soil conditioner to soil in a contained area having a water flow inlet and outlet; and planting a plurality of plants in the soil, the plants being of the same species as the plants of the test bioreactor.

Abstract: A recirculating aquaculture system comprising a microorganism growing apparatus and a method of using microorganisms to remove a pollutant from a fluid utilized in a recirculating aquaculture system. Furthermore, the microorganisms are harvested and used as a foodstuff fertilizer, biofuels, and bioplastics.

Abstract: An aquaculture system including a fish tank, a floating media bioclarifier, and a mineralization tank. The mineralization tank includes a first influent inlet for receiving sludge having a first solids concentration from the bioclarifier, an effluent outlet for returning to the bioclarifier a fluid having a second solids concentration less than the first solids concentration, and a second influent inlet configured to receive influent from the fish tank which has bypassed the bioclarifier. A hydroponic system is configured to receive effluent from the bioclarifier.

Abstract: A subsurface flow constructed wetland (SFCW) includes a sand layer having a ventilation property of 90 mL/(cm·s) and a permeation rate of less than 0.3 kg/m2/h under a two-meter-high pressure head, a filter layer disposed on the sand layer, and a gabion module disposed on the filter layer. The filter layer includes fine sand with a particle size of 0.25-0.35 cm. The gabion module includes a gabion box including a plant layer and a filler layer, and the filler layer is disposed on the plant layer.

Abstract: Systems for algae-based water filtration and algae harvesting are described herein. A flow-way comprises a channel and a divider positioned within the channel that separates the channel into sub-channels. The flow-way further includes an algal growth that grows on a sidewall of the channel and/or the divider. The algal growth can be established in the flow-way by positioning a pre-seeded mesh element within the channel, the pre-seeded mesh element having an algae culture growing thereon prior to positioning the pre-seeded mesh within the channel. A harvesting system comprises a hinged container that includes a straining screen. The hinged container is positioned downstream from a flow-way and receives water from the flow-way. Biomass in the water is strained by and accumulates on the screen. Weight of the accumulated biomass causes the hinged container to tip and deposit the accumulated biomass in a second container.

Abstract: A calcium reaction control method and device, which can adjust the input amount of carbon dioxide gas inputted into the calcium reactor according to the measurement of the concentration of carbonate ions in the solution to be tested, and input the calcium reaction water from the calcium reactor into the water tank to provide the required carbonate ion concentration in the water tank. By means of the present invention, the amount of carbon dioxide input and the amount of calcium reaction water can be controlled, which can improve the control accuracy and ease of use.

Abstract: The present invention relates to a method and a device for controlling pollutants in basin water used for irrigating farmland in extremely water-scarce areas. The device includes an alternate vertical flow constructed wetland, which is constructed 4-10 m far from basin revetment. After feeding basin water into the constructed wetland, pollutants, such as heavy metals, nitrogen, phosphorus and organic matters, are adsorbed or degraded through the constructed wetland, and then the treated basin water is transported to the farmland.

Abstract: It discloses a system for controlling heavy metals and a method for preventing and controlling heavy metals using the same. The system includes a constructed wetland (3), in which several layers of fillers are laid, so that water is allowed to flow through each layer of the filler to remove heavy metals. Preferably, a sandwich wall is constructed around the constructed wetland (3), and organic matters (12) which generating heat through fermentation is filled in the sandwich wall to supply heat to the constructed wetland (3) in winter. The sandwich wall is easy to build and the fermentation materials are cheap and easily available, thereby the present method is able to effectively solve the difficulties occurred in the operation of constructed wetland in winter.

Abstract: An earthworm reactor comprises a main body frame and multilayered reactor box bodies located in the main body frame. A bottom plate is arranged at the bottom of each layer of the main body frame, and the reactor box body is movably arranged on the bottom plate of each layer; an aerator pipe and a filtrate collecting pipe are arranged in the reactor box body of each layer; an aerating air supply pipe connected to the aerator pipe of each layer and a filtrate centralizing pipe connected to the filtrate collecting pipe of each layer are separately arranged on one side of the main body frame; the aerating air supply pipe is connected to an external aerating device and the bottom of the filtrate centralizing pipe is connected to an external liquid storage tank.

Abstract: Activated iron media and methods for generating and using the activated iron media. The method involves aqueous suspension comprising a zero-valent iron, ferrous iron, and an iron oxide to provide a settled solid and re-suspending the settled solid to provide an aqueous suspension containing an activated iron media.

Abstract: A system for capturing and monitoring atmospheric polluting agents (1) that includes a protection skeleton (100) that covers and protects the entire system; a power supply module (200) for providing electrical energy to the system; a bioremediation module (300) that captures and bioremediates the polluted gaseous streams that circulate inside it; a control and monitoring module (400), which census and modifies the operation parameters in real time and at least one particle capture unit (500) that gathers the particles that approach the system. The system boosts the restoration of polluted gaseous streams with a certain concentration of some substance that could represent a risk for the health of the people.

Abstract: A vermicomposting system for treating waste water streams that includes a pretreatment stage for converting liquid or semi-liquid organic waste streams into a feedstock for vermicomposting; a vermicomposting digestion stage having populations of worms and beneficial bacteria which consume and break down organic material and nutrients present in the feedstock from the pretreatment stage to create worm castings, vermicompost, and a liquid compost tea that contains plant nutrients, plant growth promoting substances, and beneficial bacteria; and a post-treatment stage in which the liquid compost tea is removed for use as an soil amendment or inoculant, or is further treated in a separate containment tank where nutrients and oxygen levels are controlled to increase specific bacterial and fungal populations.

Abstract: A water filtering system is provided for growing algae that filters the water. The system may include a container having a cylindrical inner surface and an opening at one end of the container. A clear central core including a cavity may be disposed inside the container and a light source may be disposed inside the cavity of the clear central core. A screen mesh may be disposed inside the container such that a surface of the screen mesh is parallel to the cylindrical inner surface of the container. The system may include an inlet configured to route water into the container and an outlet configured to route water from the container. A lid may cover the opening of the container.

Abstract: The present invention discloses a small integrated greening device and method for recycling wastewater, including a wastewater collection system, a microorganism and plant purification system, and a reclaimed water collection and distribution system. The method includes the following process: greywater or wastewater is collected through a pipeline and enters a water collection tank of a wastewater collection part. Lifting is performed by submersible sewage pumps, such that the lifted water enters a microorganism and plant synergistic purification and greening part. Each submersible pump is controlled by one corresponding automatic water level controller to transport the treated water to the reclaimed water-use sites.

Abstract: A method for treating wastewater having one or more of suspended solids, dissolved solids, biological oxygen demand includes solids filtration followed by a bi-polar/bi-directional flow through ionic module fitted with anionically/cationically charged plates followed by a sub-sonic resonance module followed by another bi-polar/bi-directional flow through ionic module followed by a ultra-sonic resonance module followed by one or more anion/cation collection membrane modules. Recycle is provided in each step, wherein each step may be repeated, and wherein one or more of the steps can be bypassed.

Abstract: A process and system for treating biodegradable waste is described that utilizes serial thermophilic and mesophilic microbial digestion to product fuel gas and a stable solid product at high efficiencies.

Abstract: A method for eliminating harmful algal blooms through optimized utilization of a modified clay method includes building a real-time state index and a standardized value grading system for eliminating a site harmful algal bloom or a harmful algal bloom in accordance with the features of monitored harmful algal bloom organisms and modified clay flocculates; acquiring corresponding grade codes of feature index values of the harmful algal bloom in a to-be-treated water body or harmful algal bloom elimination effect through the real-time site state index and the standardized value grading system; comparing the above grade codes with an expert system to obtain an operation solution for eliminating harmful algal blooms through optimized utilization of the modified clay method. The result is tracked and monitored in real time and the operation solution is optimized and adjusted in time according to the harmful algal bloom elimination effect.

Abstract: A method of using microorganisms to remove a pollutant from a fluid by exposing microorganisms to a fluid containing a pollutant, the microorganisms uptake the pollutant, then the microorganisms are exposed to a condition in order to stimulate the microorganisms to release the pollutant. Furthermore, the microorganisms are harvested and used as a foodstuff for human and animal consumption.

Abstract: A siphon type composite vertical subsurface flow constructed wetland has an uplink pool with a depth ¾ that of a downlink pool. Siphon-type drain tubes are equidistantly distributed at a first outer side of the uplink pool, and a total flow of the drain tubes is slightly greater than a largest total influent flow. Three layers of substrates are paved on each pool. A substrate on a first layer is a biological ceramsite having a relatively small grain size, another substrate on a second layer is zeolite having a relatively large grain size, and a further substrate on a third layer is cobblestone having a large grain size. The third layers of the pools are integrally communicated, and sewage in the downlink pool flows to the uplink pool through a communication port. Sludge on bottom layers of the pools is discharged from a siphon tube with water.

Abstract: Disclosed is a method for removing fatty oil from a surface containing the fatty oil comprising the steps of applying to the surface containing the fatty oil a composition comprising a sol-gel derived material, the sol-gel derived material including a plurality of alkylsiloxy substituents and the sol-gel derived material obtained from (a) at least one first alkoxysilane precursor having the formula: (R?O)3—Si—(CH2)n—Ar—(CH2)m—Si—(OR?)3??(1) where n and m are individually an integer from 1 to 8, Ar is a single-, fused-, or poly-aromatic ring, and each R? is independently a C1 to C5 alkyl group and (b) optionally, at least one second precursor having the formula: where x is 1, 2, 3 or 4; y is 0, 1, 2, 3; z is 0, 1; the total of x+y+z is 4; each R is independently an organic functional group; each an R? is independently a C1 to C5 alkyl group and R? is an organic bridging group and then moving the composition from the surface to remove the fatty oil.

Abstract: Phytoremediation processes, methods, materials and compositions to remediate soil, sediment and groundwater that is contaminated by per- and polyfluoroalkyl substances (PFAS) via phytoextraction which includes the uptake and translocation of contaminants in the contaminated media by plant roots into the above ground portions of the plants. The plants can be selected from sixteen plants as well as other plants and the invention can include managing soil salinity levels of the plants, manipulating amounts of organic matter in the contaminated site media, managing pH levels of the contaminated sites, utilizing double cropping systems, utilizing double-canopy system, and managing harvest methodology of the plants.

Abstract: The present disclosure is directed to systems and methods for tree preservation efforts by determining a critical root zone of a selected tree within an existing landscape including hardscape elements. The critical root zones can be determined based upon the diameter size of each tree being impacted. The system includes generating a landscape map including visually representing the calculated critical root zone including any root zone loss within the existing landscape. In addition, the disclosure provides a system for determining survivability of an impacted tree that takes into account a number of factors to ensure a survivability percentage of at least 70%.

Abstract: A facility for treating and recycling animal waste (2), including a unit (6) for methanizing the waste including treatment of the obtained biogases, a cogeneration unit (8) delivering electricity and heat (32) from the biogases, and a unit for hydroponically cultivating microalgae (14) in photo-bioreactors supplied by the liquid phase (12) of the organic residues from the methanization. The facility further includes a unit for cultivating macrophytes (22) supplied with water (20) leaving the unit for cultivating microalgae, and a vermiculture unit (24) fed by harvesting the macrophytes (22) and by the sludge (36) coming from the raw digestate from the methanization.

Abstract: The invention provides structures, methods, and assemblies for bioretention systems, including tree box filters with substantially permeable panels integrated into a bottom portion of the tree box filter. The invention also provides methods and additional structures that are useful for managing stormwater flow and inhibiting the flow of pollutants, debris, and other contaminants into drainage systems.

Abstract: A stormwater treatment system and method for removing sediment, chemical pollutants, and debris from stormwater runoff by utilizing bioretention practices including physical, chemical and biological processes. Stormwater is directed into a primarily open-bottomed, multi-dimensional container whereby entrained sediment and other transportable materials are filtered and treated through a media filter layer consisting of inorganic and/or organic materials. A live plant (preferably a tree) situated within the container with roots resident in the media filter layer with the ability for expansion beyond the perimeter of the container through openings in one or more sidewalls. The treated water may be further conveyed beyond the perimeter of the container by additional openings and/or piping. A vertically positioned overflow/bypass/clean out piping apparatus may be included within the stormwater treatment system to provide additional water conveyance.

Abstract: A redox water treatment method comprises first determining the composition of water and whether water treatment requires either oxidation or reduction, or both to optimize nitrogen removal by a bioreactor. Sulfur dioxide (SO2) is injected into the water to be treated to provide H+, SO2, SO3=, HSO3?, dithionous acid (H2S2O4), and other sulfur intermediate reduction products forming a sulfur dioxide treated water, which behaves either as a reducing agent or an oxidizing agent depending on the strength of the acid concentration, which alters sulfurous acid from a reducing agent to a more powerful oxidizing agent.

Abstract: The invention relates to a solid filtering wastewater treatment device (100) comprising a first stage (101) with a freely drained fixed culture arranged directly above a second fixed water saturated culture stage (105), and a force aeration system (110) extending under the second stage. The invention also relates to a wastewater treatment method, as well as a process for sludge mineralization, implementing such a purification device.

Abstract: The invention discloses a method for harmless treatment of cyanophytes and suspended solids accumulated in lakeside wetlands, comprising the following steps: first, adding a flocculant to a water body to be treated, so as to allow the flocculation of cyanophytes to accumulate in the surface layer of the water body, and settling the formed cyanophycean floc to the surface layer of sediments; second, adding a floc stabilizer to perform accumulation and compaction of the cyanophycean floc and stabilized treatment of the floc in the surface layer; finally, conducting further reoxygenation treatment on the bottom water body. The method of the invention can realize efficient and ecologically safe flocculation of accumulated cyanophytes at low cost and control odor compounds such as sulfides decomposed from flocculated cyanophytes, so as to provide a new method for harmless treatment of excess cyanophycean accumulation in eutrophic lakes.

Abstract: A method of implementing organic synthesis reactions uses a composition containing a metal catalyst originating from a calcined plant. The plants can be from the Brassicaceae, Sapotaceae and Convolvulaceae family, and the metal catalyst contains metal in the M(II) form such as zinc, nickel, manganese, lead, cadmium, calcium, magnesium or copper. Examples of the organic synthesis reactions include halogenations, electrophilic reactions, cycloadditions, transesterification reactions and coupling reactions, among others.

Abstract: A process in which a waste stream containing microbes and organic constituents is passed through a process environment comprising a solid media, microbes, and higher animals, such that some of the microbes and/or organic constituents within the waste stream are removed from the waste stream and some of the removed microbes are destroyed or consumed by the higher animals. The process environment may include an irrigated environment, a submerged environment, or a combined environment.

Abstract: A process for treating domestic wastewater may include directing wastewater into a tank containing a membrane filter and mixed liquor. The process may include recirculating wastewater and mixed liquor from a top end of the tank into a bottom end of the tank via a recirculation conduit. The process may include introducing a flow of wastewater and mixed liquor from the recirculation conduit into an aeration device and drawing ambient air into the aeration device using the flow of wastewater and mixed liquor from the recirculation conduit. The process may also include drawing wastewater and mixed liquor proximately surrounding the aeration device into the aeration device using the flow of wastewater and mixed liquor from the recirculation conduit. The process may include aerating a mixture of wastewater and mixed liquor with the ambient air below the membrane filter.

Abstract: A system for treating wastewater containing selenium has a sequencing batch reactor upstream of a fixed film reactor. The sequencing batch reactor may be operated under anoxic conditions while influent is mixed with residual sludge. The SBR reduces total nitrogen, suspended solids, or both. Selenium is removed in the fixed film reactor by biological reduction to elemental selenium.

Abstract: A common final clarifier is provided downstream of a two-stage or three-stage activated sludge (AS) system that includes: (A) one or more flow equalization basin (FEB) reactors and a nitritation reactor as the first AS stage, and an anammox reactor as the second AS stage, or (B) a carbonaceous biological oxygen demand (BOD) removal reactor and one or more FEBs as the first AS stage, a nitritation reactor as the second AS stage, and an anammox reactor as the third AS stage. A first return activated sludge (RAS) flow is conducted from the final clarifier to the first AS stage and a second segregated RAS flow is conducted to the second AS stage. Alternatively, a third segregated RAS flow is conducted to the third AS stage.

Abstract: The invention discloses an unpowered water purification system for a riverfront landscape constructed wetland, comprising a riparian wetland constructed along a lake-land ecotone of a river, lake-pond. The riparian wetland comprises a plurality of alternatively arranged wetland islands and watercourses formed between them. The bottom surface of the riparian wetland is lower than the normal water level of the river, lake-pond, and the upper surface of the wetlands is flush with the normal water level of the river, lake-pond. Plants are planted on the wetlands. A revetment is constructed between the riparian wetland and the river, lake-pond, and its upper surface is between the bottom surface of the riparian wetland and the upper surface of the wetlands. The invention achieves good purification and landscape effects. The purification system has some advantages such as good landscape effects, simple management without energy and power consumption, and thus is durable and stable.

Abstract: It discloses an application of a fermentation broth of Potamogeton crispus in the removal of nitrogen in constructed wetlands. The fermentation broth of Potamogeton crispus is prepared by the following method: collecting, draining off and grinding the Potamogeton crispuses, then, placing the grinded Potamogeton crispuses into a fermentation tank, mixing them with domesticated fermented sludge, and then adding water and fermenting the mixed liquor at a constant temperature, removing the residue of the Potamogeton crispuses, and obtaining the prepared fermentation broth of Potamogeton crispus. The present invention also discloses an application of the fermentation broth of Potamogeton crispus in the removal of nitrogen in constructed wetlands.

Abstract: An apparatus and method for the biological treatment of water using algae comprising a support frame for flat, two-sided LED lighting-panels and flat, two-sided algae turf plates, an axle, the flat, two-sided LED lighting panels and flat algae turf plates are arranged as spokes radiating from the axle in an alternating panel so that each side of each two-sided lighting panel faces and illuminates a side of a flat algae turf plate, the algae turf plates being removable from the support frame so that the collected algae can be removed from each side of each the algae turf plate.

Abstract: A method for treating and improving the quality of pond water used in growing aquatic species for aquacultural applications by adding to the pond water active bacteria that are preferably grown on site in combination with a nitrification enhancement agent such as calcium carbonate or calcified seaweed, and an optional reaction surface area modifier such as calcified seaweed or plastic or metal particles or fragments.

Abstract: A wetland roof system and method for treating domestic waste water is disclosed which comprises a container having three sections and a L/W ratio greater than 10, a gravel layer deposited at the bottom of the container at a first thickness, a crushed stone layer deposited directly on top of the gravel layer having a second thickness, a sand layer deposited directly on top of the crushed stone layer having a third thickness, a soil layer deposited directly on top of the sand layer having a fourth thickness, and a plant layer growing from said soil layer at a predetermined density.