# US 10,120,836 B2 · Gathering materials on the ocean surface based on forecasting area density > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,120,836 B2 - Document ID: US10120836B2 - Status: Granted - Kind: B2 - Application number: 15/043,251 - Filed: 2016-02-12 - Published: 2016-08-25 - Granted: 2018-11-06 - Earliest claimed: 2015-02-12 - Assignees: The United States of America as represented by the Secretary of the Navy - Applicants: Gregg Arthur Jacobs; A. D. Kirwan, Jr.; Helga S. Huntley; Bruce L. Lipphardt, Jr. - Inventors: Gregg Arthur Jacobs; A. D. Kirwan, Jr.; Helga S. Huntley; Bruce L. Lipphardt, Jr. - Web page: https://patentgrep.com/patent/US10120836B2 ## CPC - G06F 17/13: Differential equations (using digital differential analysers G06F7/64) - B63B 2211/02: Oceanography - Y02A 90/10: Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - B63B: SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING (arrangements of vessel ventilation, heating, cooling, or air-conditioning B63J2/00; floating substructures as supports of dredgers or soil-shifting machines E02F9/06) - Y02A: TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE ## Abstract Embodiments relate to gathering materials on an ocean surface. Initially, an initial distribution of material is determined based on observational sources, and the material is represented by particles in a numerical ocean model. Trajectories for the numerical ocean model are determined based on modeled surface currents data, and velocity gradients are computed along a corresponding trajectory of the trajectories for each of the particles based on the initial distribution. At this stage, deformation tensors are computed for each of the particles based on the velocity gradients, and a dilation map for the particles is generated based on a time step tensor of the plurality of deformation tensors for each of the particles. Collection of the material is monitored based on the dilation map. ## Claims ### Claim 1 A method for gathering materials on an ocean surface, comprising: determining, using a computer processor, an initial distribution of material based on observational sources; representing the material by a plurality of particles in a numerical ocean model; determining a plurality of trajectories for the numerical ocean model based on modeled surface currents data; computing a plurality of velocity gradients along a corresponding trajectory of the plurality of trajectories for each of the plurality of particles based on the initial distribution; computing a plurality of deformation tensors for each of the plurality of particles based on the plurality of velocity gradients; determining a dilation for each of the plurality of deformation tensors based on a divergence from a corresponding local velocity gradient of the plurality of velocity gradients of a corresponding particle of the plurality of particles, wherein the dilation is determined according to: 1 Δ ⁢ D ⁢ ⁢ Δ D ⁢ ⁢ t = ∇ · v ⁡ ( x ⁡ ( t ) ) , and wherein D D ⁢ ⁢ t is a total derivative along a material trajectory, Δ is the dilation, and ∇·v(x(t)) is a time series of divergence along the corresponding trajectory x(t); generating a dilation map for the plurality of particles based on the dilation of a time step tensor of the plurality of deformation tensors for each of the plurality of particles; using the dilation map to identify a target area with a higher area density; create a recovery path that navigates a recovery ship through the target area; and monitoring collection of the plurality of particles based on the dilation map. ### Claim 2 (depends on 1) The method of claim 1, wherein the dilation map shows an area density of the material as represented by the plurality of particles rendered in a geographic area. ### Claim 3 (depends on 1) The method of claim 1, wherein the plurality of deformation tensors is determined based on the plurality of velocity gradients using: ∂ F ∂ t = ( ∇ ⁢ v ) ⁢ F wherein ∇v is a velocity gradient of the plurality of velocity gradients and F is an original deformation tensor of the plurality of deformation tensors for a particle of the plurality of particles at a specified time step, and wherein a next deformation tensor of the plurality of deformation tensors at a subsequent time step is determined by integrating the product of the velocity gradient and the original deformation tensor. ### Claim 4 A non-transitory computer readable medium having computer-executable program instructions embodied therein that when executed cause a computer processor to: determine an initial distribution of material based on observational sources; represent the material by a plurality of particles in a numerical ocean model; determine a plurality of trajectories for the numerical ocean model based on modeled surface currents data; compute a plurality of velocity gradients along a corresponding trajectory of the plurality of trajectories for each of the plurality of particles based on the initial distribution; compute a plurality of deformation tensors for each of the plurality of particles based on the plurality of velocity gradients; determine a dilation for each of the plurality of deformation tensors based on a divergence from a corresponding local velocity gradient of the plurality of velocity gradients of a corresponding particle of the plurality of particles, wherein the dilation is determined according to: 1 Δ ⁢ D ⁢ ⁢ Δ D ⁢ ⁢ t = ∇ · v ⁡ ( x ⁡ ( t ) ) , and wherein D D ⁢ ⁢ t is a total derivative along a material trajectory, Δ is the dilation, and ∇•v(x(t)) is a time series of divergence along the corresponding trajectory x(t); generate a dilation map for the plurality of particles based on the dilation of a time step tensor of the plurality of deformation tensor for each of the plurality of particles; use the dilation map to identify a target area with a higher area density; create a recovery path that navigates a recovery ship through the target area; and use a global positioning system to monitor collection of the material by the recovery ship. ### Claim 5 (depends on 4) The non-transitory computer readable medium of claim 4, wherein the dilation map shows an area density of the material as represented by the plurality of particles rendered in a geographic area. ### Claim 6 (depends on 4) The non-transitory computer readable medium of claim 4, wherein the plurality of deformation tensors is determined based on the plurality of velocity gradients using: ∂ F ∂ t = ( ∇ ⁢ v ) ⁢ F wherein ∇v is a velocity gradient of the plurality of velocity gradients and F is an original deformation tensor of the plurality of deformation tensors for a particle of the plurality of particles at a specified time step, and wherein a next deformation tensor of the plurality of deformation tensors at a subsequent time step is determined by integrating the product of the velocity gradient and the original deformation tensor. ### Claim 7 A system comprising: a memory to store program code for gathering materials on an ocean surface; a global positioning system to determine a location of a recovery ship; and a computer processor operatively connected to the memory to: determine an initial distribution of material based on observational sources; represent the material by a plurality of particles in a numerical ocean model; determine a plurality of trajectories for the numerical ocean model based on modeled surface currents data; compute a plurality of velocity gradients along a corresponding trajectory of the plurality of trajectories for each of the plurality of particles based on the initial distribution; compute a plurality of deformation tensors for each of the plurality of particles based on the plurality of velocity gradient; determine a dilation for each of the plurality of deformation tensors based on a divergence from a corresponding local velocity gradient of the plurality of velocity gradients of a corresponding particle of the plurality of particles, wherein the dilation is determined according to: 1 Δ ⁢ D ⁢ ⁢ Δ D ⁢ ⁢ t = ∇ · v ⁡ ( x ⁡ ( t ) ) , and wherein D D ⁢ ⁢ t is a total derivative along a material trajectory, Δ is the dilation, and ∇•v(x(t)) is a time series of divergence along the corresponding trajectory x(t); generate a dilation map for the plurality of particles based on the dilation of a time step tensor of the plurality of deformation tensor for each of the plurality of particles; use the dilation map to identify a target area with a higher area density; create a recovery path that navigates a recovery ship through the target area; and use the global positioning system to monitor collection of the material by the recovery ship. ### Claim 8 (depends on 7) The system of claim 7, wherein the dilation map shows an area density of the material as represented by the plurality of particles rendered in a geographic area. ### Claim 9 (depends on 7) The system of claim 7, wherein the plurality of deformation tensors is determined based on the plurality of velocity gradients using: ∂ F ∂ t = ( ∇ ⁢ v ) ⁢ F wherein ∇v is a velocity gradient of the plurality of velocity gradients and F is an original deformation tensor of the plurality of deformation tensors for a particle of the plurality of particles at a specified time step, and wherein a next deformation tensor of the plurality of deformation tensors at a subsequent time step is determined by integrating the product of the velocity gradient and the original deformation tensor.