View source for MathModDB:Free Fall Model (Vacuum)

As a pedagogical example, let us consider the famous story of [https://portal.mardi4nfdi.de/wiki/Item:Q1437751 Sir Isaac Newton] being inspired to formulate his theory of gravitation by watching the fall of an apple from a tree in the year 1666. We have implemented this within the MathModDB knowledge graph by including a [[Item:Q3826|Research Field]] named "[[Item:Q3825|Pomology]]" (science of fruits) [[Property:P824|containing]] [[Item:Q3782|"Gravitational Effects on Fruit"]] as a specific [[Item:Q3781|Research Problem]]. Currently, there is a choice of two [[Item:Q3830|Mathematical Models]] addressing this problem, i. e., "Free Fall Models" [[Item:Q3785|without]] and [[Item:Q3784|with]] the effect of air drag, both of them assuming constant gravitation. [[Item:Q3785|The former one]], actually dating back to Newton, contains the simple "[[Item:Q3794|Free Fall Equation]]", 
<math>v=v_0-gt</math>, as a Mathematical Formulation. That equation contains the free fall velocity <math>v</math>, the gravitational acceleration <math>g</math>, and the time <math>t</math>. Obviously, the first and second of these Quantities are assigned to the [[Item:Q3845|Quantity Kind]] velocity and [[Item:Q3849|acceleration]], respectively. Within the context of these "Free Fall Models", several different Computational Tasks can be formulated, e.g., [[Item:Q3864|how long does it take for an apple to reach the ground]], or [[Item:Q3870|with which velocity will it hit the ground]]. While the above equation (without air drag) is so simple that it can be solved analytically, in more realistic free fall models the underlying equations have to be solved numerically which falls into the realm of the MathAlgoDB knowledge graph containing suitable numerical solvers for ordinary differential equations such as the Runge Kutta family of algorithms. Finally, we mention that also more complex models involving gravitational effects have been implemented in MathModDB, such as the dynamics of planets in our solar system.

== Testing SPARQL with staging portal ==
* Get a list of models that are used for the research problem ''Gravitational Effects on Fruit'' 

{{#sparql:
SELECT ?Model
# where Q3782 refers to the Gravitational Effects on Fruit
# where P802 refers to Modelled By
WHERE {
      wd:Q3782 wdt:P802 ?URL.
      ?URL rdfs:label ?Label 
      BIND(CONCAT("<a href=", STR(?URL),  ">", STR(?Label) ,"</a>") as ?Model)
}
| chart=bordercloud.visualization.DataTable
| log=2
}}

* Get how many models are used for the research problem ''Gravitational Effects on Fruit'' 

{{#sparql:
SELECT (COUNT(*) AS ?Number_Of_Models)
# where Q3782 is the Gravitational Effects on Fruit
WHERE {wd:Q3782 wdt:P802 ?item.  
}
| chart=bordercloud.visualization.DataTable
| log=2
}}

== Testing SPARQL with Münster Infrastructure ==

{{#sparql:
PREFIX mdb: <https://mardi4nfdi.de/mathmoddb#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
SELECT ?Label ?Description
WHERE{ VALUES ?url {mdb:FreeFallModelVacuum}
              ?url rdfs:label ?Label;
              rdfs:comment ?Description;
}
| endpoint=https://sparql.mtsr2024.m1.mardi.ovh/mathalgodb/query
| chart=bordercloud.visualization.DataTable
| log=2
}}
* List of Formulations

{{#sparql:
PREFIX mdb: <https://mardi4nfdi.de/mathmoddb#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
SELECT ?Formulation
WHERE{ VALUES ?url {mdb:FreeFallModelVacuum}
              ?url rdfs:label ?Label;
              rdfs:comment ?Description;
              mdb:containsFormulation ?formulation .
              ?formulation rdfs:label ?Formulation .
}
| endpoint=https://sparql.mtsr2024.m1.mardi.ovh/mathalgodb/query
| chart=bordercloud.visualization.DataTable
| options=
| log=2
}}

* List of Related Research Fields

{{#sparql:
PREFIX mdb: <https://mardi4nfdi.de/mathmoddb#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
SELECT ?Research_Field
WHERE{  mdb:FreeFallModelVacuum mdb:models ?Research_Problem . 
        ?Research_Problem mdb:containedInField ?RF .
        ?RF rdfs:label ?Label
   BIND(IRI(CONCAT("https://mtsr2024.m1.mardi.ovh/object/mathmoddb", "%", "3A",?Label)) AS ?URL)
BIND(CONCAT("<a href=", STR(?URL),  ">", STR(?Label) ,"</a>") as ?Research_Field)    
}
| endpoint=https://sparql.mtsr2024.m1.mardi.ovh/mathalgodb/query
| chart=bordercloud.visualization.DataTable
| options=
| log=2
}}

* List of Related Mathematical Models

{| class="wikitable" style="margin:auto"
|+  
|-
! Mathematical Model
|-
| [[MathModDB:Free Fall Model (Air Drag)|MathModDB: Free Fall Model (Air Drag)]]
|-
|}

* List of Computational Tasks using this Mathematical Model

{{#sparql:
PREFIX mdb: <https://mardi4nfdi.de/mathmoddb#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
SELECT ?Computational_Task WHERE{ VALUES ?url {mdb:FreeFallModelVacuum}
              ?url rdfs:label ?Label;
              rdfs:comment ?Description;
              mdb:appliedByTask ?task .
              ?task rdfs:label ?Computational_TaskL .
              BIND(REPLACE(?Computational_TaskL, " ", "") AS ?computational_task_without_whitespace)    
          BIND(IRI(CONCAT("https://mtsr2024.m1.mardi.ovh/object/mathmoddb", "%", "3A",?computational_task_without_whitespace)) AS ?URL) 

BIND(CONCAT("<a href=", STR(?URL), ">", STR(?Computational_TaskL), "</a>") as ?Computational_Task)
}
| endpoint=https://sparql.mtsr2024.m1.mardi.ovh/mathalgodb/query
| chart=bordercloud.visualization.DataTable
| log=2
}}

* List of Related Literature

{| class="wikitable" style="margin:auto"
|+  
|-
! Literature
|-
! 
https://doi.org/10.1017/CBO9780511818509
|}